[GeoffR]

I don't have a Mini myself so I might be wrong on the procedure for factory reset, maybe someone else with a Mini can confirm whether it would normally work, or maybe that has been disabled too somehow.

If you can sync via wifi that would bypass the problem with two different accounts in the Kobo desktop. It would be intersting to see what happens, whether it updates the firmware or not.

Edit: One other possibility: Deleting the device's database (located in .kobo/KoboReader.sqlite) should cause it to create a new one, which I think has the same effect as logging out. But since there is something funny going on with the device it might also leave you with a non-functioning Mini if it doesn't work. If you were to try this then at least making a backup of the database would be a good idea.