the 360 is externally balanced and they never put an A904 behind the 360, they always used the A727. to use a 360 with an A904 you would have to have a specially balanced torque converter.
not so, i bought a '77 360/904 combo off ebay for my dart, it had never been apart. it came from a 77 fury wagon, it actually was the desirable 904 with the extra clutches and lower gears, i think it was actually called an A999.
also you can get a specially balanced flexplate and use any 904 torque converter that you want with that.
-Tim