You give me trouble. But I'm getting better.
UPDATE: Backing up images got a little easier.
This time I backed up the text files by going to the labs page and using the export feature. I also had to back up and restore the images separately;
scp /var/www/ghost/content/images crow@offsite:
The good news is, after getting the usual 502 Bad Gateway error, I used the Digital Ocean Rebuild feature and, luckily, I could rebuild to the version I was trying to upgrade to.
Unfortunately, this does mean I had to destroy the old server, invalidating keys and whatnot. That means I have to use
useradd crow and follow the interactive prompt, and I shouldn't forget to use
visudo as well, to add crow to the sudoers file.
Then, it's as simple as recovering the image backups, creating a new ghost user, and using that ghost user to import the json file we made at the start.