If no devices are showing up like this, is it necessary to reset all settings? Or just turn off Handoff?
I suspect the reset all settings is working because it disables icloud by default. If you show no other devices under Bluetooth devices, turn of handoff on your iPhone and then sign out of icloud. Power off your iPhone and back on and you should be fine. You can also sign back into icloud. As long as no other Bluetooth handoff devices show up you should be fine.
----------
Thanks for sharing this. The iCloud thing did work for me, but I have two iPad's that are both logged out of iCloud and I'm reluctant to log them in and risk breaking the fix. I'll try shutting down handoff across the board and resetting my settings, and will see if I can then get my iPad's logged back into iCloud.
If you turn off handoff across all your devices, you should be able to sign back into icloud on them all. As long as none of them show up under Bluetooth services on your iPhone after doing this, everything should continue to work fine.