I would like to renovate this pair of powered multimedia speakers that
seems to have a real mean AC buzz. I'm guessing this is coming from
the power supply part of the "amplifier" section (if you can really
call it an amplifier ). What would be some obvious things to look
into reconfiguring to knock out the hum? (repositioning a transformer,
grounding something, adjusting where signal lines go?, etc...)

Yeah, of course it is not worth the effort really to bother, but I
would like to make this a sort of pet project that maybe I could learn
something out of.