Update to the update: I am an idiot.
The reason the coaster wasn't working was that the regulators were falling out of regulation. I'm so used to working with LDO regulators these days, I was caught out by the 317s needing a full 3V to regulate. They were just bareeeellllyyy on the edge of falling out of regulation, hence the buzzing-that-comes-and-goes phenomenon.
I only found it after taking the board upstairs and plugging the wall-wart into a different variac (that was set lower than the lab downstairs). LOUD buzz. Turn up the variac: no buzz. The good news is this is an easy fix, the bad news is that it means we're looking at 30V/15V rails, which will reduce the maximum output of the amp a bit, and change some schematic values. On the other hand, if I want to go realllllly simple, I could go to fixed regulators, but fixed regs are pretty mediocre until you go exotic (that is, far beyond the LM/MC7815 series).
So, maybe you'll see a chapter after all!