As I've said a few times.  You REALLY need to think in terms of a decentralized system (where there is no identifying information available at all about the hasher), and in terms of a Sybil attack.  Until you can get your mind into that mode, you aren't going to come up with any useable ideas at all.

Note, that it took decades of people thinking in terms of a decentralized system under a Sybil attack all failing to come up with a solution until Satoshi came up with the proof-of-work secured blockchain idea.  If you seriously start thinking in terms of a decentralized system under a Sybil attack the first somewhat workable solutions that you'll come up with will all be "proof-of-something" (work, stake, storage, etc) solutions.  All of these will have the same feature of a fixed reward for completing a fixed proof.