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).
No, there is an unexpected twist. Any block of height t containing N txns maps to exactly the same satoshis. The lottery is deterministic rather than random. The only random element is who happens to have their computer online. We could predict who is going to mine in advance. This isn't necessary to think about, but in theory the whole mining process could be scheduled because of this.
However, once the block hash is signed by the first winner, then the block contents cannot be modified by the other winners. By default, the group is not supposed to sign more than one version of block t. They could cheat and sign a very large number of versions of block t with N txns.
Three cases if they cheat:
1) If one version has already been built upon and the other blocks are orphans, then keep building on the longest version.
2) You are aware of more than one version, but haven't seen any that have been built on. In this case, combine any two duplicate blocks t and mine a 'null block'. The record of the cheating is put in the blockchain. All txn for time t are ignored and you move on to block t+1.
3) You are only aware of one version. In this case try to build on it until you hear about another. (You don't know that cheating has occurred yet.)