Still no luck tracking this down, but more evidence that it's interference and not coming from the outlet/circuit.
• I shut down all phones, computers, tablets, and unplugged or took the batteries out of any "smart" device throughout the house. Unplugged everything else on that circuit (just a few lamps, and a turntable, receiver, and tuner, all of which haven't been on during other tests). Still chirping.
• Chirps seem dependent on location. It chirps when keeping the amp in the same location, but powering off of different house circuits. Conversely, there are location near outlets on other circuits in the house where it doesn't chirp, and if I run an extension cord from the original outlet to this location, still no chirps.
• I walked out a rough grid on the floor of the office where I'm set up, and the chirps are definitely louder near the outside wall of the house. It varies in intensity at different locations, but not in any other sort of pattern that I could figure out.
For what it's worth, my home office is on the 2nd floor of a 100+ y.o. house in a relatively dense neighborhood (Phinney/Greenwood in Seattle, for anyone who knows it). Powerlines maybe 40' out the window, and a neighbors house ~20'. Pigeons right outside the window, but they don't appear to be radio collared. I don't know, stabbing in the dark here about what the source of interference might be.
I'm on a mission to figure this out now. But I guess the more practical question is: is there anything I can do about it (short of moving my office to a different part of the house)? Is there anyway to shield the amp, somehow?