In my proof of concept, I solved it using shamir's secret sharing. What you do is for your device, you share your keys across a bunch of "friends", so say you share your key with 5 friends. If you lose your device. You can restore by contacting 3 of your friends. All your data that we store on our service is encrypted with your private key which never leaves your device. When you recover your key, it will then download your encrypted backup and decrypt. Your friends must be forced to confirm, so to hack you. Someone must hack all your friends devices at once or get a hold of their physical devices to authorize restoration. You actually only need to setup once on your phone. To login to ipad, PC or any other device, you would use your phone the same way folks used it for 2FA today.

http://www.multipasskey.com/susdemo/