Ok, I think I finally have it sorted out. The amplifier stage is really sensitive to the characteristics of Q104.
Now when I had it working great for a few minutes the other day - before the big flame-out of R105 - I was using a 2N5416S transistor that I thought was going to be a really good match. Those transistors are quite pricey, so after the flame-out, I replaced it with one of those fell off the boat" (NTE) parts, an NTE397. The NTE transistor apparently has really bad Icbo leakage at these high voltages. So once I was pretty confident this was the source of my over-current problems in the negative channel, I replaced it with the second 2N5416S that I had on hand. I've put some heatsink compound between it and its heatsink, and I'm carefully watching its temperature while I run at max output. I'm hoping the first burnout of this part was just a fluke, or a side effect of the resistor problem (see below).
The second thing I did was to replace the output driver transistors with ones with lower Hfe. I'm using the same NTE part, an NTE124, just two I selected that have Hfe of 17 and 23. Based on the specs for the OEM transistor, I think this will be a bit closer, and I am hoping to get the amp gain back down to closer to the original amount, so that these oscillations will go away. If not, we'll have to look at some additional caps to frequency compensate it.
Oh, also forgot to mention earlier that R104 was bad as well. It's tucked away behind the big yellow filter caps, so I didn't initially check it. When I did, I noticed it was reading about 30% high, so I went to replace it. As soon as I touched it with the hemostats, it crumbled.
I've had the whole thing assembled, semi-calibrated, and running now for about an hour, with no issues. I think next up will be the electro-mechanical clean-up - clean the PCB, clean the switch contacts with De-Oxit, etc.