I’d also like to point out that banning the accounts and deleting the spam posts is all well and good. However, some of the spammers have links in their profiles, which are visible from Google as well as from inside the site. So even if their profiles have been banned, they’re still serving a purpose.
phpBB3 has an expansive and highly customizable permissions system. (Sometimes this isn’t a good thing.) It’s possible to give someone enough control without giving them too much. (It’s also possible to give someone too much unintentionally.) Fortunately, it also has a pretty good system of permission inheritance, which is great when adjusting permissions on an existing install with this many forums in place already.
There are a lot of active, mature users here who wouldn’t mind lending a hand. All it would take is a couple of mod installs, just to tighten and clean things up a bit, and to increase the permissions for two or three of them (for redundancy). Matt has already volunteered. Could possibly look to capmikee, Ghalev, Juhana, Victor, Felix, Jim or Robert, among others, as knowledgeable, (mostly) level-headed and very active, if any of them are interested.
Just that while the forum isn’t flooded with spam yet, it certainly isn’t getting any less frequent. And as more time passes and the site gets more popular, it’s very likely to get worse if unaddressed.