Using the RCA cables grounds one chassis to the other. Using the balanced evidently does not. Either the balanced sockets are floating on one or both ends or your balanced cables don't have a connection from end to the other for the body of the shells which would ground them. If using the RCA cables grounds everything and that solves the hum then I don't see why you can't do that. If all the equipment has three prong AC plugs then that would also ground them together.
BTW, your equipment draws more current than the P600 is designed to provide.
BTW, your equipment draws more current than the P600 is designed to provide.