Never heard an amp do this before, ideas?

OP,

This is not a “tube” problem. Not sure what it is… but this is never problem with high end audio equipment. So, either it is a PrimaLuna problem or a location problem. I would not abstract this to tubes or good quality components.

When you say "apartment", it makes me think of multiple households and things that are beyond your control in those dwellings. Though you probably have separate meters, some god-awful faulty appliance or wiring flaw could be generating interference. 

Can you take it to a friend's home, Along with a pair of headphones and see if the problem exists away from your environment?

"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!