Almost all 12v motors will have a 5/16" shaft but that's an easy fix (as you said...drill it out by 1/16"). There are some inexpensive 12v heater fan motors that might work. Example:
https://tinyurl.com/2u9tx2ck And a common speed controller like this one would be handy (you may not want the motor running at high speed all the time):
https://tinyurl.com/mwc3evh6Hope this is helpful, John.