Okay, so after listening for a while tonight I noticed the transformer started buzzing again. The makeshift isolation transformer made no difference, and if I press on one corner of the transformer, it goes dead silent, whereas if I press on a different corner it gets much louder. Seems like it only starts doing it after it's warmed up a bit, which is why it seemed to go away when I was only doing short listening sessions.
The new bias scheme is pretty cool though. I'm being cruel and using the K1000 on it, which sounded kinda hazy and dull with the original LED biasing, but sounds quite lovely now. I'm using some 1.9V green LEDs I had laying around for a bias of 2.6V.