I just managed to get myself out of this problem. Still not sure why it worked, but here’s what I did:
While using auto-upgrade, I got the “Fatal error: Call to undefined function: is_admin()” message.
Tried to roll back, but couldn’t get my backups to unzip properly. So…
I went back to the error page and hit my browser’s back button.
Instead of the previous upgrade page, I got a page with an “upgrade your database” button. I clicked the button.
It took me back to my admin pages with a warning at the top to get rid of extra files from an old installation. I clicked on the link to do that.
The upgrade page reloaded, said I was done. And my blog seems to be working again, and upgraded!