Look at the 500 small block Mopar auto OD. They were a factory trans that was a 904 with the OD and lockup converter in one unit. Mopar put them behind the V8s, and they could be built to handle some pretty high power outputs.
I thrashed the he!! out of a 904 behind a pretty well built 340 for a few years and I've had a 318 with the 500 behind it that had towed a car trailer around for a while, I wouldn't be afraid of putting a built one behind your 360, and factory stuff should be available. Gene