After rather a lot of flailing about because of some things we'd forgotten to do, or test, or that we'd remembered and went sideways anyway...
...most stuff works now. Some better than it did. The mailing lists are now on mailman, yay.
However, sending mail through my SMTP server probably doesn't work. The new settings will involve TLS and/or SSL and port 587, fwiw. I think. I'm now too tired to be smart about it, so it's time to go splat and track that last problem down...later this morning.