Joe, I'm really, REALLY hesitant to give advice about other's gear but it sounds like solder joints need to be re-flowed. Assuming your cables are perfect, AND assuming all your gear is powered from the same circuit, AND assuming there are no weird grounding issues between components, there should never be audible hum from audio gear, even faint hum.
Every time I've chased down on-again/off-again issues it turned out to be solder joints. I've never seen an issue on machine soldered hifi boards but the hand soldered boards on some hifi components can be problematic. Assuming they are built by someone competent, tested upon manufacturing, work fine, get boxed up and shipped, in use they can can develop a problem. I've seen solder joints that look fine, and test fine with a meter but dont pass the press on the board test. Put some pressure on the circuit board even just a little and the connection becomes intermittent.
When I had my AV company, amps got re-capped and re-flowed every three years. Those amps worked balls to the wall all the time, and their "work week" would include powering subs at 2 ohms in 100 degree outdoor heat for 12 straight hours, get packed in a truck, bounced to a city 10 hours away and do the same thing the next day. (would love to see a hfif amp try that...) ridiculous dubstep bass, wonky generator power, on and on... I learned to be proactive about maintenance. Solder joints are always the place to start.
Pat