Well, I took the advice and rebooted after 4 hours. When I powered back on the screen said ‘swipe up to upgrade’, so I did. I just woke up and 10 hours later it’s the same bright screen with the Apple logo and the progress bar at the very end. I can’t use iTunes to try and force a restore or set up as new because it claims ‘Find my iPhone’ must be turned off.
I just rebooted for the last time. It’ll have to go back to the store I think if this happens again. If nothing else, I can either confirm burn-in or put minds at ease if this thing does set up appropriately. That Apple logo has been static on the bright screen for 15 hours straight.