’Ground loops’ (and grounding issues in general) can be tricky to diagnose.
Don't say that!

I've ordered an inexpensive isolator (~$10) just to try it out. I'll start there for an easy fix, but I'll also try your suggestions to test the problem.
Does the amplifier have a two or three pin power plug into the wall AC?
Excellent question. I believe it's two but I'll check next time. I'm pretty sure it's a built-in power cord and those usually seem to be ungrounded. It's also not a very high-end model so who knows where they cut corners?
Is the subwoofer itself grounded?
Nope and I wouldn't know how.
Have you tried non bi-amped mode on the sub amplifier?
I have not! I'll give that a shot. It's not like I need all 200 watts considering the small children who live in the house.
Have you tried connecting everything (everything including all things plugged into the other receiver inputs) to the same power bar, into a single AC outlet?
Everything is on a single very long power strip with about 12 outlets on it.
Disconnect as much stuff as possible from the receiver. Minimal or no input connections - Play an FM radio for sub-woofer testing
I'll try that, but I only have two inputs as it is (Tivo and Apple TV). I guess it's possible that this is coming in over the coax on the Tivo...