Update: I sent the circuits to the mothership, got them back about a week later with a couple mods to the filter board, and the oscillation is gone. I kinda miss it in a perverse way. Not really, but it was fun through delay and reverb!
The buzzing was still there, but a bit of copper shielding tape and that was taken care of. I don't understand why Modulus did such a poor or nonexistent job of shielding back in the day.
Thanks, Mica and crew for the quick turnaround! The bass sounds fantastic now!