How warm is the pot getting? Like "ouch", or just barely noticable?
The way it's wired (between the amp an speaker) it's always disappating a Watt or so. I'll play mine some this evening and see how warm it feels...
So I kinda assumed, once we found out that something on the sound board is pulling the -12V down (or up), that it made the most sense to address that first. The implicit hope was that fixing whatever caused that would also fix the humming.
So: you've now replaced both LM741s, and something is still pulling the -12V to -4V when the sound board is plugged in. All that right?
If so, then it seems to me that one of the following must be true:
1) one or both of the DACs (U19 & U20) are bad and dragging the -12V line.
2) something else, that I missed on the schematic, which uses -12V is bad and pulling it down.
3) there's a short somewhere on the PCB that's pulling the -12V down (up).
I think you mentioned recapping the sound board. Which caps, specifically, did you replace? Have you double/triple checked your work for proper polarity of those caps?
Also, you might try putting a DMM in resistance (ohms) mode on the -12V & GND line of the sound board. If there's a dead short (or nearly so), you've got something to look for.