iPhone stuck "Removing iCloud Data..." after iCloud sign out

After an hour I decided there was something clearly wrong, so this is what I did to resolve it:

1. Powered down (long press on the top button, slide to power off),
2. Powered up and entered password,
3. Opened Settings (I appeared to still be still logged in to iCloud, but iCloud was off - it seems that things were just half completed in the original sign out),
4. Signed Out of iCloud again (this time it finished almost immediately).

The In-App-Purchase test then worked fine.

What I did was to:

1. follow what @Ali Beadle's approach
2. from another iOS device, go to settings and delete the iCloud Backup for this old device

After 2) was done, the signing out is immediately done.