Database update complete and working. The first few scripts gave errors, but I assume it's because I didn't have 2.2.0.4 after all. My system gave that version, but I guess I had 2.2.0.6 or .7, because after that, all the scripts worked and my site is now up and running on the new database.
Now I'll need to make some work on the front end to add back my customizations, but all seems fine for now.
Thanks a lot!