Didn’t read the entire post but I think the characterization of PCP’s is a bit off - some SNARK constructions and STARKs both use PCP’s - using a linear PCP vs a PCP doesn’t impact transparency or proof size, that’s more a function of the commitment scheme
It seems like a VRF might be a more natural choice than a commitment scheme for verifiable randomness, since it doesn't require any honesty assumption for participants, and Keybase already manages keys (though maybe it would be a problem if participants could change keys midway through the ceremony).