OK. I think I've rescued it. I did a complete permissions overhaul and created a new theme based on the stock one (only changed a single image in it thus far - it will be a bunch of work to finish it). I have not seen any spam registrations since I setup the Q&A registration plugin. (And I can lock it down tighter if need be - waiting on a release version of a Bad-Behaviour mod for phpbb3 - I expect it will be along soon...)
So, I think we're back in business.
Jeff, SFHQ, Frey, we'll need to meet on TS and discuss this so we're all on the same page.