> I understand some AC motors can be operated on DC.

Most Brush motors are actualy "universal", eg they can work on AC or DC.

 > I understand the [rewound] motor will not perform as well on 12 V.

Not so, as long as it is properly rewound, it should work just as well. Of
course, as the volts goes down, the current must go up, so it's possible the
brushes may not handle the current.....

BTW, I would think it would be simpler to build a simple 12 Volt to 120 Volt
inverter. Either AC or DC.

.................... Zim