Never heard an amp do this before, ideas?

"I tested two primaluna amplifiers, both did it. I also tried a cheater plug."

This tells me not to waste time on the tubes or components in your amp, unless it does the same thing in a totally different environment. Heck, take it to work and try it there.

What's a cheater plug?

@mwinkc it's a (not very safe) bypass on ground, so you can rule out ground loop issues. I think you're right, it's environmental. Unfortunately I don't think it's related to electricity, it's probably radio interference. Because the only thing that made the sound almost go away was wrapping the thing in a faraday blanket.

The disappointing part is that I can't fix that-- it's probably coming from outside. So I'm wondering if SS will be as sensitive to RFI, or if I can get away with hybrid.

Keep the inputs plugged in! Problem solved! 

Take the amps to your local stereo shop to check out some speakers with it.  Gives you a reason to go listen to some speakers.  Maybe even to work with a pair of headphones.  Eliminate the environment.

You would not be using expensive speaker cables, would you?   I'm recalling back in the day, there were speaker cables that certain "tube" amplifiers did not like. Would set the amp into oscillation.  My idea was that the circuit were seeing a resonant tank circuits of their tubes, transformer and speaker cable. Try going back to zip wire or other cable. 

I second @jasonbourne52 suggestion. Does it make the noise when the inputs are connected to something and amp is powered on?