That Was Pretty Easy
Network services are already back up (obviously, as I’m using a client computer on my network to submit this entry).
SMTP is up and running with the proper trappings, and I’m now using the correct server, Postfix.
IMAP, IMAPS, POP3, and POP3S are all working. The wonderful imapsync is currently running on my VMWare backup image to synchronize my message backup with the new server. This is working flawlessly.
Still need to get fetchmail, MySQL, Apache 2.0 (!), and cowsay up and running, but those aren’t too hard with apt-get at my fingertips.