What fixed the Loading... with a backup was while your phone is 'broken', go to settings via the notification center, go to backup and untoggle the apps backup. Now do a backup from your device.
This will lose your installed apps, but if you now do a hard reset and use that backup all the rest will still be put back in place except for your apps (which is most likely the cause of this mess).
Update: looks like the apps arent installed, but they are in the store but show as a failed installed. Strange.
Looks like this is the fix then:
1) While your phone is stuck on Loading... head over to the notification center and go to settings
2) Browse to settings > Update & security > Backup
3) Untoggle 'Backup my app data to OneDrive'
4) Tap on 'Change OneDrive backup settings'
5) Tap on 'Backup now' (sometimes it doesnt start immediately, a few taps/moments waiting should kickstart it, you'll know it started when the button is replaced by a progress bar)
6) When the backup is finished, do a hard reset
- Power the device off
- Press the power key once, device will vibrate
- Immediately press and hold the Volume Down key
- Exclamation point will appear, release Volume Down key
- Press these buttons one at a time in this order: Volume Up, Volume Down, Power, Volume Down
- Device should vibrate, reboot, show the Nokia flash screen, and then go to the spinning gears install screen.
7) When it asks for the backup, choose the one you made
8) Wait for the restore to finish, then head over to the Store app (NOT the beta Store)
9) You'll see your old apps in the downloads section, they show as failed (in my case there were 54 apps).
From what I can see it's the start screen that keeps crashing and trying to restart over and over again. When a WP app crashes it closes and returns to the previous app (or start screen). This is exactly the case, it crashes and keeps going back to the previous app (the start screen), thus an infinte loop.
I found this by opening the settings, and then pressing the home button (so not closing the settings), The start screen opens with 'Loading...' but crashes so the phone goes back to the previous app (in this case, the settings app).