Rebuilt 904. Whirring. Dead?

A whirring sound like that is generally an internal leak. Either a blown clutch pack seal or converter problem but your statement that it does it with the engine shut off and you just pushing or towing the car would seem to rule out the torque converter because it isn't doing anything unless the engine is running. To tell you the truth unless your trans. is an older model with a rear pump I don't know how it could possibly make any noise with the engine shut off. I'd first check the rear differential. Jack the car up and put it on stands and spin the wheels and listen where the noise is actually coming from. If you can't tell by spinning it by hand start it up and run it through the gears. Yanking the converter out and replacing it without any diagnosing is not the proper way to do things.