Yesterday, I finally got around to adding the two amps to the ground bus on the Triton. Since each amp is on its own circuit, and the source gear and Triton is on another circuit, I was a little apprehensive about creating a ground loop. However, with no input, and the volume near max, it is dead quiet.
I listened to the complete grounded stereo for hours last night, and it's playing now. There is no negative effect in my system by having everything grounded to the Triton, even though the Triton is on one circuit, and each amp is on its own circuit. While I have no measurements, I get the impression it plays a tad louder so I am using a few db lower volume settings. There certainly seems to be a clearer, sharper, detailed sound now. Or more accurately, those existing traits are a bit more enhanced now. This is a pretty good tweak which only cost the price of spades, and cutting up some old 10 gauge speaker wire.