So before dragging a cable across the house to connect the AVR up to our refrigerator's chassis ground, I decided to bring my UPS over (which has a TVSS ground screw) and try using that for the grounding point.
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I plugged the UPS into the wall (not the Furman, though I don't think it matters), ran some small 18AWG from the TVSS ground to the phono ground on the AVR, powered up the AVR, powered up the KEF speakers, and...
silence!
Well, relative silence - there was still some hiss if you listened for it - but no more buzz! So hot damn, good call
@McFly!
Now, interestingly, when turning the AVR off and leaving the KEF speakers on, I still got a harsh buzzing from the KEFs. Nothing near as bad as it was before (it was so loud prior to running this ground cable that I worried it would damage the speakers over time), but still audible to the point of being disruptive.
I didn't plan on having a UPS as a part of my AV stack, but if it keeps the speakers from buzzing I'll do it. Are there any more permanent solutions now that we seem to have the culprit identified? Seems like I just need to find a way to permanently ground the AVR chassis, right?
Thanks again to everybody that's taken time to read this, weigh in, and offer advice. This is why I love communities like this! I seriously can't thank y'all enough - it's been a stressful past couple months, and having something that's supposed to be enjoyable (listening to music / watching shows to unwind) turn into a stressful, frustrating, seemingly unsolvable problem sucks. I'm overjoyed to be making progress on this!