Is there such a thing as a low-profile garbage disposal? The exit pipe from the disposal is about 1/2" lower than the 'out' drain pipe that goes into the wall. Lowering the drain, well, I just had new cabinets with granite tops installed... the existing drain also goes through a stud in the wall...

First, can you cut 1/2" off the outlet of the disposal and make it fit?

If not, try turning trap around and install it backward. That will give you about 1".

The exit pipe from the disposal is about 1/2" lower than the 'out' drain pipe that goes into the wall
I know all know low-profile garbage disposal all. If we're talking about the bottom end and of the disposable discharge tube than simply follow Harold advice a great back to fit. Good luck, Tom