Thanks for the awesome repair guide. I snagged a practically brand new TE off of Ebay for $34 and managed to fix it with a $1 part from Radio Shack.
It got a little hairy there for a bit though. I thought I was being careful but still accidentally pulled the negative trace off the board when I removed the capacitor. Thankfully the trace ripped pulled up far enough for me to follow it to another solder point. The leg of the little transistor/MOSFET that sits just adjacent to the cap will work.
If I had it to do over again I would definitely have tried to touch the soldering iron to the legs and gently pry them up rather than trying to pull the cap off cold.
Looks so innocent just sitting there.
Disaster strikes! I did not notice the little trace that was ripped out of the surface of the board at first - I honestly thought it was just a strip of paint or glue or something. The scratches you're seeing where the pad for the negative trace was are my desperate attempts to find what the pad had been attached to. I was hoping that if I dug into the board I would find another solder point. I realize at this point that was silly, but at the time I had no idea.
But that was exactly what I needed to find an alternate soldering point.
Here is the alternate soldering point magnified some more.
I decided to remote-mount the cap because the connections, while solid, were so fragile I didn't want to risk any more bending and twisting than I had to. It may not be pretty but it works like a champ.