My snap judgments:
Invision looks really feature-heavy, but I question how many of these features we really need. There seem to be a lot of permission/moderation/tight-control functions that seem a little unnecessary on a board of this (relatively) small size and good-natured membership base. That it costs money also hurts.
Phorum looks functional but just a little sparse. It reminds me of more primitive web boards and i-got-problems.com; this is not a bad thing, just a pretty big change from the current system, and not one I'm sure I all the way like.
vBulletin looks pretty robust, but it also doesn't quite sit right with me. There seem to be a lot of bells and whistles we just don't need on these things; the "related threads" bit in particular struck me as weird. Once again, it looks good for really big impersonal boards, but not for here.
Zorum is getting closer, but still feels a little... rinky-dink and impersonal, I guess. It kind of rubbed me wrong.
UBBthreads, Simple Machines, and Vanilla strike me as the most viable options. Vanilla is extremely vanilla, and is very old-school and texty; I would miss the avatars, but otherwise it seems very robust. UBB has a slightly weird feel, and SM is a little gingerbready, but both have lots of potential.
My important criteria:
1) Converter availability. I don't want to lose the stuff already here.
2) Easy/cheap-or-free for Jough. Nothing hugely expensive, nothing too difficult.
3) The basic PHPbb capabilities remain intact. This means... like, quoting, reliable read/not-read notes, stuff like that. Avatars are also good, although smilies I can truthfully live without.
I think this raises a question, though: do we want this new board to feel like the old one? I do, but I have no idea if I'm in the majority or not. Thoughts?