I believe the described system would work fine without needing double spending. Even simply acquiring the bids to verify transactions into the chain could make

I believe the described system would work fine without needing double spending. Even simply acquiring the bids to verify transactions into the chain could make it worthwhile. When the "selfish" chain is published, it takes two blocks of transactions from anyone else, plus it has given the "selfish" miners the entire period from when they last discovered a secret to when they played their hand to mine for the block that will follow. It may allow them to capture a greater portion of the main chain by denying information to other chain agents unless beaten or trumping. Actually, that would be a good term for the method. "Trumping" the chain.