Okay, so there was a long database operation I started running last weekend; I had decided to abort it, clean up, and try again next weekend. But I think something about one of the database indexes (used for boosting performance) was not entirely cleaned up, because now any site operation which would use that index (mainly annotation exports) takes way too long and brings the infrastructure to its knees. So now I'm trying to re-run the aforementioned operation to completion, hopefully fixing the problem. My estimate for that operation is 5-6 hours, and then I'll have to check if that was actually the fix.
Apologies for having this happen during the weekdays, this was the result of a few missteps I made during some maintenance that turned out to be rather complex.