The issue i see off the cuff, is that PGP keys are pretty large, especially if using the 4096bit version.
You could simply use the fingerprint of the key instead. It's only a few bytes. The key can be safely stored on a key server somewhere, or some distributed hash table if you want to keep it decentralized.
I'll have to do some research, and maybe reach out to my one friend who is a cryptographer and see if they have any suggestions. GOOD IDEA!

Hope it will help ;-)