Miners do not have control over what hard for users adopt.
So the solution is really very simple:
Pay miners to produce blocks without transactions in it and eventually to ignore blocks produced that include transactions.
How much do you have to pay them? Probably 3x the times the value of BTC transaction fees.
How will bitcoin respond? Increase transaction fees.
How would it help Bitshares if we funded such an attack? It wouldn't. We would be labeled by the market as a bad actor and no one would want to join us.
Miners have control over if transactions are put in the main chain. Ultimately it doesn't matter what hard forks a full node adopts, the miners are the final source of authority, and the only way to wrest this control away from them is a hard fork away from the main chain to another blockchain with a different mining or consensus algorithm (which bitshares incidentally is). Also bitcoin doesn't have a system that will allow the different actors in the community to work together to counter this. Even if they could, and they made some sort of weird wallet hack that refused to relay any empty blocks or something like that, the SHA-256 hashing power vested in seeing the exodus through will likely merge mine attack any forks to protect their own gains.
We will pay them drastically more than the transaction fees. An average block with a block subsidy of 25 has about 0.1 BTC in transaction fees. We (or another attacker) will pay the early ERB's 100's of bitcoins, and eventually 50 BTC per block (or whatever numbers we decide will give us the highest success rate). There is no possible way that the bitcoin community will be able to compensate miners more than this if it begins to become apparent that the migration will go through.
The way this would help us is that once bitcoin transaction stops, people will have no option but to use their new bitcoins on the bitshares blockchain. Undoubtedly some will ragequit and sell everything, but overall the average BTS shareholder will gain significantly and bitcoin holders will also gain in the long run because they now get the benefit of DPOS and the rest of bitshares (including less inflation in the long run). Even if the entire thing falls apart the amount of publicity we will gain will end up giving us a massive boost to our market cap. I don't think we have to worry about being labeled as bad market actors, we're already an evil altcoin that they wouldn't buy into no matter what. The shitstorm will not be bigger than if bitcoin died on its own and bitshares became huge and started having major infrastructure defect. Also, if we fail others will follow with the same attack (but just even worse conditions for the bitcoiners so that miners are sure to support the exodus quickly)