Google contacts stopped syncing
So, as the night progressed, and I tried various fixes such as what Nathan suggested and restoring from Titanium backups and such, my problems simply got worse.

I ended up simply backing up my application data and restoring from a nandroid backup.  That seems to have fixed it.  It may have been a virus, or I might've corrupted something somehow.  After I restored the backup, the contacts are syncing just fine.