Creating a transaction that is all fees for embedding hashes?

[dillpicklechips]

I was thinking about https://www.proofofexistence.com/ and was wondering if it's possible to create a transaction that is either all fees that includes a manual hash in it or a transaction that includes a hash that is somehow up for grabs by anyone after a set amount of time or even a transaction that is spendable by whoever notices it first?

Would doing that allow hashes to be stored yet still allow the transaction to be pruned for thin clients? Or would the blockchain bloat be pretty much the same?

[Sukrim]

Use hash to calculate private key, send coin to corresponding address, send coin back... Done.

To give proof: reveal hash, calculate private key again and present the transaction that already took place.

You pay miners twice for the transactions and you are not worse off concerning pruning than before, potentially better if you combine inputs for the first transaction.