I just recently finally started digging into this thing again. I removed all of the amp caps and started testing a bunch of traces and vias, but I didn't find anything else obviously bad. I put it back together and was going to try BlueBMW's suggestion of following the schematic and probing for audio. But after plugging it up with a new AV cable, I actually found that it worked pretty well! Turned out, the left audio channel on my other cable is flakey. So that was part of my problem.
In testing it for a while, it seemed good until I realized that the sounds from the ADPCM channel were very quiet. Looking at the multiplexer schematic, I saw it was handled by IC503. That's the one I removed to repair a couple vias when I did the cap job.
I took some voltage readings, and confirmed that it had ground on 8v on pin 8. But where the schematic says it should have 2.5v on pins 3 and 5, I'm getting about 3.8v. And in checking the other pins, they're all reading 3.8v also.
So I'm not really sure where to go from here. Does this sound like a bad opamp at IC305? And is the high voltage on pins 3 and 5 a problem?