Good news: wrapping TT around that joint about 12-14 times finally caused it to stop leaking. All the joints seem watertight now.
Horrible news: Still leaking, though not at a joint. There's apparently a small crack in the main casing which is letting some water through. I emptied it out and put some aquarium sealant on it and I'm waiting for that to dry, but i have no idea if that will fix it.
Thanks for the help to everyone who has been offering it. This is seriously one of the most frustrating things I've ever worked on. I can't win with it!