With the exception of a couple of sets of photos (which I can easily replace), I’ve been able to extract everything essential from the image of the crashed disk.
To recap, my hosting company deleted everything on the backup server without telling me, and when there was a hard disk failure on the actual server a few days later, everything was gone. I did have backups from much earlier, but it would have been a lot of effort to replicate everything from that.
Fortunately, they managed to recover the original hard disk image, and the only unreadable files so far have been unimportant ones.
If you find something broken, please let me know below!