I think it would be great to continue the thread after the game comes back. There's a tendency in-game for some characters to get shown more attention and interest in others, in terms of asking them about their personality and backstory and so on. That can make people feel bad, and this thread gives them an opportunity to talk about their character without needing someone to specifically ask them.

But it definitely seems like it'd be a lot of work to keep running indefinitely, so why not turn it into a forum game? Something like the "grant the wish of the person above you" game, but instead you're answering a question posed by the last character who posted, and then ending your post with a question for the next character.

That's something I hadn't considered, and a good point. Maintaining the thread isn't too much effort so long as I prepare questions in advance. It would help with longevity still.