So, I re-soldered pin 9 on the C socket (the left channel) and when I tested it, both the L and R channels sound the same (which is good). Thinking that the problem was solved, I removed the jumper between the 3 pins and the 10/11U and the problem came back (L channel is weak). So, I re-installed the jumpers and the problem went away again.
What should I try next?
Also - I hope this helps - I keep suspecting that there's a problem with the C socket. While music was playing just now, I touched the tube in the C socket and got a ton of crackling noises. If I do the same thing to the tube in the B socket, nothing happens. I also noticed that if I applied light pressure to the C socket that there was a large volume drop. Again, doing the same on the B socket produces no change.
To go back to the very beginning of this thread, I had suspected all along that there's something wrong w/ the C socket - it's either a bad solder joint or something with the socket itself. So, before even opening this case, I re-soldered the whole C socket. When doing that, I believe I accidentally swapped the wires going to the shunt regulator. I believe that this is why I started this thread thinking that the issue was with the shunt regulator (as it was measuring wrong).