I've had a look at SMF, installed it on a VM and imported the database backup from here - no real issues. Will have to download the forum attachments (1.3 GB), forum avatars and the homepage as well as the download section from somewhere - SSH/FTP access would be handy if available, worst case I should be able to grab things via wget.
We can transfer the domain to me - will need an auth code from the existing registrar to initiate this. If we do this first, we should be able to keep the disruption minimal.
There will be some minor costs involved in setting this up and running it. Not much, I expect perhaps 10 EUR a month or so for hosting and domain registration as well as a one-time transfer fee. Will absorb this for now and we can maybe set up a contribution PayPal account to cover it later. Obviously I'm not looking to make any profit from this.
tiger79, thanks for offering, will make you a moderator when things are moved over if that's ok.
What did I forget?