Again, I appreciate your help. Yes, the Adwords rep I talked to on the phone said there was nobody who could help me figure out why our organic results tanked overnight, but that I could ask on the forums. I'm not prepared to do that at this time.

There were two changes that happened on the same day, at least one of which I'm sure is the cause: we pushed out a ton of pages we had generated from old data, and we had a regression whereby our international sites lost their canonical tags on links. It's pretty clearly our fault, but it would be nice to have someone spend 30s saying, "this is what triggered the issue; don't do this" rather than, "no we can't help you, maybe some random person on the Internet can".