I already had explained this and I don't understand why it is so difficult for you to comprehend that the payers must send a PoW with their transactions. The majority of the PoW comes from payers, and the payers have every incentive to approve the longest chain, so their transactions are included on the block chain. If an individual payer wants to attempt a double-spend, he doesn't have enough PoW by himself to accomplish it.
Profitability of mining has nothing to do with the incentives in my design. I hope I don't have to explain this again.
Again you miss the point entirely. An individual payer CAN have a majority of PoW in exactly the same way as it can happen in bitcoin, except you've totally removed the incentive to use this power for good instead of evil.
Tell me this: how can a recipient know when it is safe to accept a transaction in your design?
Same as in Satoshi's design. When the acceptable number of blocks have been confirmed since the block that included the transaction.
Define 'acceptable' - you will find it impossible because there is nothing to value the PoW being expended.
You can't have branches which don't conflict on double-spends without a total ordering. You can't get total ordering without LCR unless you use a clock to timestamp each node of the tree. Period.
What does it mean to have a conflicting double spend? (a double spend is itself obviously a conflict, so you mean a conflict of conflicts?)