No worries, thanks anyway!
It does seem strange that it's such a hassle to get an app installed that the company itself has made.
Anyway I think it may be down to the Android version, because two colleagues of mine were able to remove their primary Google account, no factory reset necessary, and then the app installed fine. But they're both on Android 4.x. Or it could possibly be a Samsung vs. HTC issue, I know at least one of them has a Samsung.
I guess I'll just have to consider if a factory reset is actually worth getting the app installed. My concern is also that it may keep doing this with every update of the app.