I assume this is some kind of proprietary connector, not a variety of the "standard" NEMA plug?http://en.wikipedia.org/wiki/Power_plug#NEMA_5-15_.2815.C2.A0A.2F125.C2.A0V_grounded.29
I'm guessing there are 2 wires hooked to the motor, and a 3rd is ground. Run the 2 motor wires to the hot and neutral of a NEMA plug. If possible, preserve hot and neutral, if they were already identified in your current wiring. The only time I could imagine it would be a problem is if the original has neutral connected to ground on the TT. I don't believe they're supposed to do that, but who knows what they did back when. An ohmmeter will confirm for you if neutral is isolated from ground.
The 3rd wire is almost certainly ground. The principle you're trying to adhere to is that of a single point ground. The idea is all grounds go back to a common point. This way, currents on one wire do not induce noise on a different part of the circuit, and ground loops are eliminated.
You could ground the equipment through the AC cord, but if you do that, you should not ground the TT at your amp. If I was in your situation, I would probably choose to ground at the amp, and just use a 2-wire power plug to the motor. That's how my Dual 1237 is wired.