I got bored of procrastinating the matter and migrated my server to a new machine - including the mail setup. My old machine ran FreeBSD and I used Jails to create subdivisions in the setup. ezjail (shoutout to erdgeist) made that easy enough. From time to time the setup inside the Jails broke, though, making updates difficult, and I’m more familiar with Linux - so my new machine runs Debian.
Migrating the mail setup was easier than I thought. But then again, I’m using only Postfix, Dovecot and a delivery to the Maildir of a standard Unix user account with some aliases. Postfix is configured suitably paranoid, of course, and does not try to be compatible to the 1990s. This might influence your server’s spam rating (just saying…).
It was thus only a matter of installing said programs, migrating the config - some paths are different, which is annoying -, creating the same user, copying the Maildir in /home and pointing DNS to the new machine. Done. I was pleasantly surprised.