Success! Posting this from Android 9 on the same phone.
After the second attempt to manually install Android 7 (which worked), I removed a couple of apps just in case, and went back to the updater. It took a few tries to download (one seemed to stop, and i had to restart to make it go again), but it was applied, rebooted, and took a while with white-ring update screen.
I hit the never-ending blue dots screen after that, and restarted by holding down the power button, but it booted and logged in fine after that.
The other thing I did differently this time round was a “basic” update rather than the “advanced” route, but I think the issue is more just things being a bit intermittent maybe…
Thanks for all the help, glad we made it with a bit of persistence and luck!