De acordo com o Auswärtiges Amt, parece que o seu único curso de ação é perguntar à "autoridade estrangeira" do estado federal em que você está estudando (grifo nosso):
[...] visa applications must be approved by the relevant foreigners authority in Germany, i.e. the foreigners authority in the place where the applicant intends to take up residence. If the approval of the foreigners authority is necessary before a visa can be issued, the procedure can take up to three months, in some cases longer, since the foreigners authority will often consult other authorities (e.g. the Federal Employment Agency). Missions may only issue visas once they have obtained the approval of the foreigners authority.
[...]
The foreigners authorities are also responsible for measures and decisions pertaining to residence law for foreigners already residing in Germany. Foreigners authorities are not subordinate agencies of the Federal Foreign Office, and the Federal Foreign Office cannot influence their decisions. They are in fact accountable to and operate under the supervision of the respective interior ministries and senators of the Länder (federal states).
Fonte: link
Infelizmente, não consigo encontrar nenhuma informação na Internet para indicar se eles receberiam sua solicitação favoravelmente, o que talvez signifique que não receberão. Por favor, deixe-nos saber como acontece.