I'm currently running a West Marches style game. I realised before I even began that, if I were to use the standard resting times, I would either have to run an excessive number of random encounters, or have each and every one steam-rolled by a fully-rested party.

My solution was quite simple. I changed short rests to 8 hours (and renamed them to simply 'rests'), and completely removed long rests, instead saying that, at the start of every new session, the party is fully rested. Because, in the West Marches format, every session is a new one-shot (of sorts), and every party starts and ends in town, it seems natural that the party should start each session rested (having just been staying in town).

As a result, each session contains a reasonable number of encounters (including traps, environmental hazards, etc.), such that the 'adventuring day' is in fact split over a week (or so) of in-game time. This keeps the number of random encounters each (in-game) day feeling natural (one or two), while still taxing the party's resources towards the end of the session.

It seems to be working well, although I foresee that resources could be stretched rather too thin if the session were allowed to run on longer (than about 6 hours), or an adventuring day were allowed to run across multiple sessions.

In theory, it would be possible to do this in any campaign, as long as the players were willing to accept the slight implausibility of being fully-rested at the start of every session, regardless of circumstances. The key is recognising that it is the long rest, not the short rest, which has the greatest potential to imbalance the game. Because recovering hit points in short rests is tied to hit dice, allowing your party as many short rests as they like is unlikely to radically affect balance.

Para resumir: The 'adventuring day' need not be an actual in-game day. It can instead be recast as the time elapsing in one session.

Encounters are not necessarily combat

What page 84 in the DMG actually calls for is "6-8 encounters" not "6-8 combat encounters."

You state that the party is into things other than combat. There are plenty of encounters that call for a non-combat use of spells and abilities (or non damaging spells) that you can present to your players. Do a few of these, have the party take a break / eat lunch, whatever (in-game) and proceed on.

1. Finding things (Detect Magic, Locate Object, various skill checks for investigation).
2. Persuading NPC's (Spells like Suggestion, various illusions, Zone of Truth, Deception) or Intimidating them.

3. Meeting NPC's and engaging in various forms of parlay that are linked to a goal, quest, objective, or a particularly important piece of information related to their quest or adventure.

   • The core skills are going to be the Wisdom based Insight, Intelligence based Investigation, and various Charisma based Skills. Spells for use on such occasions will need to be cast with care.
   • Zona da Verdade needs a lot of set up if it is not to get people's guard up, unless what you are doing is an interrogation rather than a negotiation.

   • Amigos e orientação (in my experience, more the latter than the former to boost the party face's chances at persuasion) can sway the interaction, as well as sugestão. The latter is more effective IMO than pessoa de charme in terms of getting someone to tell you something they know but were keeping hidden.

   • The goal of these encounters is information. (Was the queen really in the necromancer's chambers, and why? Who is it that is recruiting these cultists?) Lastly, if you actually use language as something that matters, the spell línguas is immensely useful in negotiations. Used it a lot in previous editions. A few months back in 5e, the cleric in our party completely defused a confrontation with a pair of hill giants by using tongues to talk to them and convince them to grant us passage through a narrow defile in the mountains. (Aside: if you don't use language differences as a world feature then a number of spells, feats, and abilities become moot.

4. Exploring an area to find the old tower rumored to be in the forest but that nobody has a map to, and might not even exist
   • Since you asked for examples: This is where simple spells or invocations like fala com animais can allow the party to gather clues from the animals who live in the forest. Detect invisibility, e até mesmo batida, can fit into such an exploration where the objective is to find something. The party is clue hunting, so descrição is a huge part of your role as DM here, and the "rule of 3" is probably your best tool in terms of getting the clues to line up so they have a chance to find it. Simply finding Esse lugar becomes the adventure's goal. Does anyone use fala com plantas anymore? Trees are very old. They may know something.

Use of the deadly encounter

Toss in some Deadly encounters that they need to use spells and abilities to avoid or flee.

1. Example: need to burn that web spell, or that wall of stone spell, or that fog cloud spell, to hold/slow down the Hobgoblin platoon so that the group can wwithdraw / flee since the swarm of Hobgoblins is too much to handle. Live to fight another day!
2. Example : Similar situation with a large enemy/hostile force, but the PC's need to turn it into a running battle so that they can use missile / bow / ranged spell fire to whittle the enemy down so that it can be taken on.

3. Example: similar situation to 1, but a risk can be taken to use various forms of persuasion, bribery, or negotiation (magical and otherwise) to utterly avoid combat.

   All of the above are encounters that can earn XP (DMG p. 261) without going for the video-game-attrition-model of adventuring via bloodshed.

Final note on sandbox style games: having deadlier encounters that include stuff to stay away from (whoa, we tripped over the annual Ogre county fair, and there are five dozen of them with more coming down the road) is part of sandbox play.
Sometimes, the world will kill you.
You can't expect to win all the time, so you have to use your wits and pick your battles.

Reverse XP budgeting: why 6-8? Do 3 (tougher) encounters with 2 short rests

usando o XP-per-day-per-character table in the DMG, you can work backwards.
Example: 4th level can handle 1,700 XP-per-character-per-day, in theory, before resource exhaustion. (The 6-8 design + 2 short rests is all about resource exhaustion / expenditure). With five 4th level characters, there are 8500 XP worth of monsters to play with for an adventure day. Le't put together three encounters with a short rest between 1 & 2, and between 2 & 3. You've reduced your problem of "how many encounters" problem: each encounter is a significant challenge. Deadly is estimated as 2500 XP for 5 level 4 characters on the XP Thresholds by Character Level table. (The below examples add up to 8400 XP all told; close enough).

1. Encounter 1: An Acolyte (re-skinned as a low level shaman) and 3 Berserkers. ((3 x 450 + 50) X 2) = 2800.

2. Encounter 2: A Druid, 3 Scouts, and a Veteran (possibly elves who are guarding a sacred grove; and xenophobic regarding outsiders). ((450 + 300 + 700) X 2) = 2900.

3. Encounter 3: A wight leading a zombie ogre and four zombies emerges at sunset from the forest / swamp / cave / ruin ... (700 + 450 +200) x 2 = 2700.

   Caveat: each of these has a lot of enemies, so "focus fire on one enemy" becomes a less effective tactic, and the DM has a bit more work to do in each encounter. Dropping in a CR 7 monster (~ 2900 XP for one encounter) presents a different problem, but is at least easier for the DM to run).

Natural Disasters and Weather

You can use the environment -- flood, rock slides, earthquakes, terrible storms, forest fires, stampedes of herd animals, locust swarms, etc as challenges that will require some use of spells for protection or to get where they are going.

• Experience with sandbox play:

  One of the nice parts of the AD&D 1e system's tables was in dreaming up encounters in a sandbox/random encounter style. That merchant caravan? It might be the next quest trigger, it might be a slave caravan (looking for more merchandise) or it might be run by a syndicate that needs more guards since some ran off last week ...

Some classics here

1. Add a clock. Make sure that PCs have a reason to press on despite lacking resources. I know it seems obvious, but not all adventures are written this way.
2. Move up to "Hard" and "Deadly" encounters. A Hard encounter should inflict some damage and force PCs to use some abilities and HD to recover.
3. Build in counters to your PCs. Creatures with Fire Resistance can really slow down that Fireball launching sorcerer. Creatures with Legendary resistance force your PCs to really burn multiple spells / abilities to win. Creatures with advantage on saves vs. magic are similarly strong.
4. Go wide. In 5e, lots of little monsters can still deal a lot of damage. 29 kobolds are a Medium encounter for 4 PCs at 5th level. But with positioning and some basic tactics, they will require multiple resources from the PCs. Also make sure one of them gets away to warn others (see clock above).

Gritty Realism, as provided, in the DMG is fine

If you want to throw less combat encounters at your players, you can adjust the rest period according to what the DMG suggests, and you will be fine either way.

When modifying the durations for resting, so that you can deal with your issue of reducing the encounters per day, you have to understand the core purpose of rests in the context of D&D. Let's jump into it.

D&D is designed a game of attrition

As you said, the DMG expects you to throw 6-8 Medium to Hard encounters per adventuring day at the players. Much of the combat system of D&D is rest-based. Despite the emphasis on roleplaying in this edition, at its core, D&D is a game of attrition.

Your options are limited by design

When you desire to reduce the number of encounters per day, you are fundamentally going against this core feature of the design. That is why there are so little options for you to take here. This is like taking the D&D combat engine (the attack rolls, saving throws, ability checks, HP, spells, etc) and discarding it: the result is not something D&D was designed to handle. Keep this in mind when you fiddle around with encounters per adventuring day, because you are ultimately affecting the attrition aspect.

A game of attrition falsamente implies combat should be challenging

The fact D&D is designed this way keys DMs off that, somehow, subconsciously even, if there is no significant attrition in the game, it's not a challenge. If the players don't start an encounter at full resources, they aren't being pushed hard enough. It is easy to see why a lot of DMs think this is true. Having an "I Win" button is not challenging, but being able to barely pass under the bar is exciting. So, combat has to be difficult, right?

No, this is false. While D&D was designed around attrition, attrition does not imply challenge, nor does it imply fun. Your goal as the DM is to get everyone to have fun, and exciting combat is just one facet of that. And a party running low on resources going up against a seemingly powerful enemy is just one type of combat.

Rests are there to reset the attrition

At the end of the standard adventuring day, an adventurer should be exhausted of their resources and have nearly no HP left. Rests were put there to refill the players, reset the attrition, and have them go on the next adventuring day right away.

This goes back to modifying resting in D&D means you are modifying a core feature of the game. Shortening the rest period (the Epic Heroism variant, for example, allows 5-minute short rests and 1-hour long rests) means you want amoras attrition in your game, in that the player characters will have more opportunities to suffer this effect. Lengthening it (the Gritty Realism variant) means you want menos attrition.

At the end of the day, you are going to have to choose: do you want more attrition, or less? Once you answer this, you can go on to modify the length or a rest. But usually, you should not modify the length of the rest if your reason is not related to this aspect.

On failing to keep up the 6-8 encounters per day rule

Your concern is that long rest-based classes, particularly spellcasters, become unfairly advantaged over short rest-based classes, when the 6-8 encounter per day rule is not followed. This is not a reason to change the duration of your rests because it is a concern over class balance, and not about the intensity/frequency of attrition in your games.

Instead, you must realize that attrition does not mean the same as challenge. Fun combat is just one way to engage the players, and attrition-specific combat is only one type of combat you can run.

Combat focused on narrative

Consider these other types of combat, which can be engaging regardless of the current resources of the party:

• A combat between the party and one of the party member's mother, who has been possessed by an NPC. There is no way to un-possess her without killing her, but she is hostile and is capable of killing the party.

• A combat between the party and someone they hate, and have hated for so long that they are now just dying to kill this NPC. However, at the last minute, and possibly even after the NPC's death, they realize they were essentially Severus Snape -- a bad guy who did bad things for the right reasons, and who had been secretly helping the party all along.

• A combat between two members of the party. This is in-character PvP, and it is always engaging (if your players are mature enough to handle the tension).

Balancing the short- and long- rest based classes

Your real problem here is the balance between classes, and not the duration of the rests. So you have to address your problems directly:

• Nerf the spellcasters. Nerfing the players is generally not good, but if you want to keep them at the same power level as the short rest-based classes, this is one way. The cleanest way I have seen this done is keeping the player characters at unequal character levels: the casters are always one or two levels below the rest of the party. It didn't cause much issue in the game, but the caster did seem quite limited compared to the rest, and I think the player didn't enjoy it that much.

• Buff the non-casters. The better solution is, of course, instead of nerfing the strong guy, you empower the weak guy. Try and give the weak player an item that would put them on par with the casters. How I've done this is I've assigned everyone in the party a different item, but each item actually evens out the DPR of all the player characters, if used optimally and in tandem with the character's abilities.

  For example, I've given an Unearthed Arcana Warlock with the Moon Bow invocation a magic bow that would let her shoot an arrow as a bonus action, in the same campaign as I gave a Matt Mercer-style Gunslinger a 1-bullet pistol that had a +8 to-hit bonus, as well as a wand to a cleric that gave them double their spell slots and access to damaging-non cleric spells (it was a one-shot). Though I don't have my notes with me anymore, I calculated the DPS from all three characters to be roughly the same, taking into account Moon Bow's ability to smite with spell slots, and the Gunslinger's insane accuracy and Action Surge, and the cleric's access to new offensive spells.

  Obviously, you will need to focus your campaign on more intense combat to justify giving your players items this powerful, but perhaps you can do better with weaker items.

• Adopt Gritty Realism (if you also want less attrition), and just narrate over the long rests. This works really well because you don't have to manufacture anything new. Just tell the players, "you can do one major thing over your week of downtime, tell me what it is." And then move on from there. You will be able to follow the GR schedule nicely here by following this pattern: 2 encounters in a day, then sleep (short rest), and then 2 encounters the next day, and sleep (short rest), and a final 2 encounters, and downtime (long rest). GR really is fine without modification.

Conclusão

Your problem is not with the rest duration, but with class balance. Address the class balance issue by nerfing the casters or empowering the non casters. Change the rest duration only when you also have decided you want more/less attrition in your game, but recognize that changing the rest duration doesn't directly solve your problem.

They do not mean every single day.

The resource system for DnD is built around attrition, nuke damage is often very high, and many abilities are overwhelmingly powerful, DnD compensates by making these abilities limited use. So 1-2 encounters per day just does not function as well as the recommended 6-8. Like KorvinStarmast's answer states, they do not all have to be combat encounters, but most of them will be.

Not all random encounters with monsters need to be resolved through combat. A 1st-level party of adventurers could have a random encounter with a young dragon circling above a forest canopy in search of a quick meal, but the characters should have the option to hide or bargain for their lives if the dragon spots them. Similarly, the party might encounter a stone giant roaming the hills, but it might have no intention of harming anyone. In fact, it might shy away from the party because of its reclusive nature. The giant might attack only characters who annoy it. - DMG 86

But that does not mean every time you travel to the next city your group must slog through 50 encounters. When you are trying to strain the resources of your party, you do 6-8 encounters, but you should not be doing this every day. Often travel can be completely skipped, if you want to show the danger of traveling in the wilderness, use one day of combat. Otherwise simply throw in a few encounters just for fun, but do not expect them to strain your party or use up valuable resources

Sometimes the destination is more important than the journey. If the purpose of a wilderness trek is to get the characters to where the real adventure happens, gloss over the wilderness trek without checking for encounters along the way. Just as movies use travel montages to convey long and arduous journeys in a matter of seconds, you can use a few sentences of descriptive text to paint a picture of a wilderness trek in your players' minds before moving on. - DMG 106

You decide when a random encounter happens, or you roll. Consider checking for a random encounter once every hour, once every 4 to 8 hours, or once during the day and once during a long rest-whatever makes the most sense based on how active the area is. - DMG 86

Also, I believe you have misread. The DMG states:

THE ADVENTURING DAY
Assuming typical adventuring conditions and average luck, most adventuring parties can handle about six to eight medium or hard encounters in a day. - DMG 84 (emphasis mine)

It is saying, don't throw more than 6-8 combat encounters at a group unless you want to kill them.

Sadly a lot of current 5e is long rests and "you keep what you kill".

Restoring balance for me occurs if you have them go out further into the world and roll on encounters, and also put more emphasis on where they are.

If they use more short rests but they are going from point A to point B:

• Throw in a side quest with some NPCs in need of help.

• Put a time limit on how quickly this needs to get done.

• While under fire (under pressure) do not let wizards get long rests.

  That alone might push an extra day or two on resources if time is now a factor.

  Combat is not the same as questing(exploring) and you can reduce encounters with more side quests that open up the world. Not being at full strength is taken care of when you need to be somewhere and failure is not an option.

You might want to take a look at the Sword Coast Adventure book for some places to visit. If this is homebrew there are so many places you can go if your party is willing to travel.

One option would be to interrupt the party with an event every time they attempt a long rest. Throw a small, easily winnable encounter at them. Fighting or casting spells resets the period for a long rest. I find this method especially effective if the party is currently in a dangerous wilderness or a dungeon where eight hours of uninterrupted rest is unrealistic.

Another option would be to introduce a deadline element into your adventure. For example, the party must complete what would normally be a ten-day journey in seven days to arrive at the village before the orc armies do. Any combat delays, even one a day, during this journey reduce the party's chances of making it on time if they insist on taking a long rest every night.