The site is now running on new hardware, new software and in a completely different location.
I think I managed to preserve all data, but if you see anything missing or not working, please let me know.
The main driver for the upgrade was the persistent problems in the forum, which meant that the first post was not displayed. This led back to an old version of Kunena, which was no longer being patched. We couldn't update to the new version, because the PHP installed on the machine was too old. We couldn't update PHP because the machine's operating system was too old. We couldn't update the machine because of the services running on it.
Does it remind you of a song with Henry and Liza in it?
Anyway, we're up and running on a new machine, using Docker as an underlying software provider, so we should not have this issue again. As a bonus, we should also find that the new machine is faster. ;)