Till - that was done. The main complaint is that the 'upgrade.php' didn't actually get rid of courier. I had to do that by hand. So, what happened was that despite the fact that _dovecot_ worked, ISPConfig happily went on its way and nuked everything in the mail folder.
Oddly enough, I had to touch every user manually as well; otherwise, the passwords refused to work. So, if I hadn't caught it, I could have ended up deleting 590 gigabytes of email just to fix the password authentication.