I've been looking. Beyond getting a server, which we could probably just get another Linode instance for, I found
hMod (which is being superseded by
Bukkit, but that's not out yet) which allows you to add your own plugins to Minecraft, all in a deliciously simple looking API which handily includes MySQL support and many more lovely things.
I've haven't had a proper look at the documentation, but I imagine it can't be too hard to write a plugin to integrate with Beehive's user authentication then we can force people to register here before they can play on Teh Mine and do things with permissions n'shit.
All we need to do is get a server and install hMod on it and get someone to write some Java to create our plugin.