Looking at your post there:
5) With any given iteration there is a chance of moving to block t+1 and starting the process over again.
If I understand correctly, any txn (above threshold of 210 coins) modifies the hash and thereby derives new lucky stakeholders who may sign the block, who would thereby move the blockchain to the next block t+1. If that's the case, how is it different than PoW mining? Any "miner" with large computational power could just tweak some txn (that he sends to himself) until the block gets solved. Each tweak attempt derives new pseudorandom lucky stakeholders, so it's equivalent to PoW hash attempts (actually PoW hash attempts at an extremely low difficulty, because creating ECDSA signature for the txn can be done quickly, so the competing "miners" will cause huge network sync problems).