After wasting my time last night, I realised where I’d gone wrong. It appears that the Google Apps Installer on the Fairphone installs the Google Apps as System Apps. So they can’t (easily) be removed and the factory reset does nothing to them.
So what I need to use is the /system/app mover and BusyBox to make the system apps into user apps.
I have tried this with iFixit and successfully removed the default version and upgraded to the F-Droid version.
Going through the actual Google apps will require a little more care and may take some time.
Now I’m confused. I’ve just glanced at the phone and the Google Apps appear to have vanished. The only thing I can think is that, when I restarted the phone, some cleanup happened. But the apps are removed, which is what I was trying to achieve, even if I’m not entirely sure how I achieved it.