With all due respect, I don’t believe this is a duplicate. My problem is that port 6667 isn’t responding at all, which as far as I can tell is mentioned nowhere in that thread.
EDIT:
Curiously, the Chatty application on my computer has the exact same issue - it is never able to connect on port 6667, and instead falls back to 80 every single time.
Sigh, maybe time to switch to web sockets?