Many thanks to the hive mind — the problem is resolved!
Having tried all these suggestions and getting no obvious result, I dug even deeper and started disassembling component parts. When I opened the Mac mini case, I found a 1/4” long strand of wire that had somehow got between two ground points. Removed it, and no more godawful noise.
Ground loop indeed, in a strange place I’d not have thought to look. The varying nature and lack of 60Hz component threw me completely.
Moral of the story here is: Listen to your fellow users, and don’t discount anything.
Thanks again!