Looks like that's a decent clue. I think your theory about a bad switch or relay is looking more and more likely...now, which one? 🤔
I power cycled the meter to remove the case. The voltage was immediately closer to 0. It didn't change much for a few minutes, so maybe not heat related.
I switched back and forth between 2W & 4W, and then back to DCV. -11.9V is back now.
Power cycled again, started immediately climbing back to -11.9V.
Switched to ACV, audible relay click, now the meter won't go back to -11.9V in DCV.
U139 is still running hot at around 92C. I don't think it's the cause of the issue, but it might be a symptom.