Is it possible to medically reclass and stay at your current duty station after AIT?

It's possible if they have a need for your new MOS at your level, but once you hit MAR2, you're needs of the Army.

You'll be sent TDY enroute to your next duty station. Expect your class date to be within 60 days of the decision from HRC. Generally you will not return to your post. You have no say in this

Definitely needs of the Army.