Old but very customized Master bathroom remodel (circa 1992)included twin drop-in sinks & exclusive use of Hardin polish brass fixtures. Hardin now long out of business. Want to replace with new bathroom fixtures. When installed over tile in 1992, the rear rims were installed such that there is just a 2 inch space between the sink rears & the tile back splash---which worked then & left just enough space (the 2 inch gap) for the Harden spouts to fit in. Today's replacement hardware requires more. Have found suitable faucets with a circular base that are 2 1/8 inches in diameter. Is there a way to cut/shave/sand paper (or any idea) the rears of the existing sink overlaps to create space to fit in the new faucets? Trying to keep this a low cost project and do not want to replace existing sinks, counter & backsplash tile