I thought I'd update, I never did solve the problem. I ended up bringing the keyboard to a repairman, who thought he'd solved the problem replacing a couple caps, but fast forward $150 in repair hours and the keyboard still drifts. I left it for a week in the same spot and every once in a while would turn it on and watched it fall a few full steps.
The other day I left it on for an hour and a half and it drifted a quarter tone.
Does anyone have any ideas of what I should test in the guts?