Don't think it is possible with your Lathe.
The main problem is first determining what type of motor you actually have and what the circuit details of the controller are.
The Term DC motor can cover a multitude of designs, both with physical forms of commutation and electronically controlled commutation on permanent magnet units, suspect you may have a form of the latter.
Had the original design been capable of readily providing a reverse function I would have thought that for the sake of a flip switch it would have been added as a sales gimmick if for no other reason.
As mentioned above I don't see any great advantage in reverse sanding, using some form of rotary sanding, preferably slow speed sanding is more effective at treating rouge grain patches.