Evidently there is a ground path missing somewhere without the RCA cables. There is no standard for XLR connectors or balanced cables. Some have a line connected to chassis ground and some do not. Evidently somewhere in your system it does not since using the ground from the RCA connectors gets rid of the hum. I wouldn't call that a ground loop since making the connection quiets the hum.
I don't see all of this as a problem, but if you are curious and since you have an ohm meter, with the P600 unplugged from the wall, check continuity from the Wadia chassis to the VTL chassis in each configuration;
1. with the RCA
2. without the RCA
Check from the Wadia and VTL chassis' to the ground pins on their power cords, The cords, from one ground jack on a P600 outlet to the others. By the proces of elimination you should figure where the ground is missing. However, I don't know how your equipment uses the ground pins on the power jack or XLR connectors, so if the piece is isolated it may not use it. Everything may be normal and your particular setup just needs that chassis to chassis ground that is missing. To save money, use a cheap set of RCA's or go to Radio Shack and get some cheap RCA plugs and some thin interconnect wire. Take 2 plugs and solder a wire from the ground lug only of one RCA to the other and use that as your ground path.