So, if you pick up and move speakers, but leave the wires, the new speaker at the same wire location will hum. But if you leave the speakers and switch the wires at the receiver, the hum disappears?
Essentially, then, the interference only occurs if a wire is connecting one particular receiver connector and one particular physical location?
That makes no sense as a ground loop issue even if you look past the "only on one output" question, unless the ground loop is caused by the location of the speaker somehow.
Is it possible you have mounted the speaker to a conductor, either a pipe or wire run or metal stud and it's now conducting power from either the coax or power strip through the speaker transducer and wall? Most speaker housings are not conductive, I know. (Also, this answer doesn't explain why the hum doesn't jump receiver outputs to whatever speaker is at that location unless you also have an AVR fault)
Do you have an oscilloscope? You could monitor signal from each AVR output and confirm it still happens even when no speaker is plugged into the humming output and/or confirm it's really 60hz and a ground/power issue and not some other interference.