Hmm. I think I found a good option. The Harbor Freight Hercules drills are only about $50 (and sometimes there's coupons), and it comes with gearing for 600 rpm output (a good option for 8" wheels, keeps it under 15mph), and a speed controller. I'll have to start with one to test the wiper voltage to make sure it's based on 5V and not the full 18 of the battery, and to make sure it'll work off of just +/- contacts without the other two pins). I might ask my dad to borrow his for the test, but $50 isn't that much for a test. I don't know how much their power rating is, but I imagine it's sufficient that 4 of them, one on each wheel, should be good. Sometimes I'll only be using two of them, but that still should be plenty of power to move it methinks, just perhaps at a lower speed.
20v Lithium-Ion Cordless Compact 1/2 In. Drill/Driver - Tool Only (harborfreight.com)