Okay, slight my bad here. Update, and also for anyone finding this later
I took the relay out, had a fifteen minute fight with it trying to pry the little %#$@ open gently, gave up and forced it, sanded the contacts with fine sandpaper, put it back in.
The noise is still there, but DC on one channel that was a bit wobbly has now settled down, so cleaning made some difference.
Of course, then I searched AK for relay cleaning info and found, (a) I shouldn't sand it, and (b) if I do should flush it with deoxit afterwards and (c) relays need adjusting sometimes.
At this point I think I'll get a replacement and just swap it out - I'm really not sure if I made things worse in the long term by scraping off coatings or leaving sanding dust in there, or thumping it around to open it, so for parts cost vs risk, I'm thinking a new one is best.
I did the volume thing, but didn't get any noticeable results - small/mid-sized test speakers though.
Thanks for the help everyone!