Please answer to my posting: Your attack still assumes that you can split the internet. That you can dictate what blockchain each miner can see.
No need to "split the internet". The attacker simply withholds the block, on Tycho's server, that are being solved by the miners. Remember that these miners are not connected to the Bitcoin peer-to-peer network. There is no need to isolate them.
But you have to distribute the block in the whole mining pool to generate the next one.