Now that the site's back, and I don't taste bile anymore, here's what happened (roughly, I don't have the energy to give more details if they exist.)
First thing's first: If you received an incorrect e-mail about your account expiring today, please ignore it. There might be a case here and there of a paid user who signed up before the backup we used was made. These will be solved ASAP.
During the maintenance job to expire old accounts, a glitch had hit the system which set the expire times on everyone's accounts minus three years. Then they were all expired. That might have been set by a glitch earlier in the day. We're sure it's a software glitch, but have not narrowed it down (all account related tools have been disabled until our staff can get some sleep and then do a careful audit tomorrow.) completely yet.
We restored from a backup a little less than a day old. Now things are peachy.