I tried re-soldering the board, but I believe I screwed it up in the process. I overheated some of the contacts, and some of the pads (the small metal contacts around the holes in the board) fell off.
I just got off the phone with a JVC parts distributor in my area, and they quoted me $151.20 CAD incl. shipping for a whole new convergence assembly.
A lesson for people who are attempting this repair: DO NOT OVERHEAT THE CONTACTS WHEN DESOLDERING. I learned that lesson the hard way. If you've never soldered before or are an amateur (like myself), read up on soldering/desoldering technique or pick up a book. Google is a great resource.
I'm not sure if I'm going to go ahead and purchase the new assembly and repair the TV, or just buy a whole new one, but I will post updates if I decide to repair.