Sorry slightly off topic, You can't tow a supra on its rear wheels because its an auto, yes, this is correct, but this is only because the engine isnt running, I always thought the drive for the pump is up by the torque convertor that spins with the engine, so if the engines running, so is the gearbox oil pump. Otherwise how would it build up pressure to engage a gear when the car is first started, if the pump was connected to the drive of the axle, and the car didn't move it would'nt have any pressure to engage gears.
So don't worry, unless you engage neutral when the engines not running and the cars moving, no damage can be caused.
As for the noise, Put the spare on the front of the car on each side seperatly to see if the noise dissapears, I had similar problems when I damaged the inside of a tyre wall on an old car of mine, its suprising how much noise it made, the inside of the tire had completely fallen apart and was rolling around in big chunks inside the tyre.