Thoan here, the original poster. I've overwhelmed by how many comments have been made! You guys have too much spare time!
The hum/ground loop is source-independent. You can also disconnect the C712's outputs and still get the hum -- it's passing through the Power Control cable, and yes, I am using mono 3.5mm cables for this.
In the course of messing about with cables and DeOxit, I was down to one Power Control cable, going from the "out" jack of one MC7100 to the "in" jack of the other MC7100. The C712 was not involved at all. Both power amps were turn on manually at the time (obviously, as there was no 12v control signal), and both hummed. (The old joke: Why do they hum? They don't know the words . . . )
I also grounded the gear together with wires attached to the chassis, something that worked pretty well in the C28/MC2105 days, but not any more.
So the hum is being introduced by the Power Control wires -- even though this circuit is independent of the signal path. Wow.
If I had some mono 3.5mm jacks on hand, I'd try making my own connectors, and maybe include a diode or two just for kicks -- next Mouser or All Electronics order, this happens. And long term, I could see making an Arduino-controlled set of relays to turn the amps on x seconds apart (there is more gear than the pair of 7100s). But I'm with Occam here, I'd like the simple solution to work.