Edited the OP.
Turns out the attack isn't possible. The assumption that miners can always mine empty blocks that the main chain has to accept is mistaken. Developers would release a full node update in response that rejects empty blocks and there would be a network partition if this was ever attempted.
The good news is that it means no one can perform this attack, so we won't be at risk by some competitor or mining pool creating a bitcoin 2.0 blockchain that destroys us. This also means that bitcoin will never be able to upgrade its consensus algorithm away from POW, and will have to die eventually, which is a shame.
I'm going to continue trying to figure out of this kind of attack can actually be done, because I still think controlling miners with the prisoners dilemma has the potential to work. But if I come up with anything I'll post it straight to the bitcoin community instead of here, to avoid negative connotations of us discussing a bitcoin attack amongst ourselves. If it turns out a hard fork can be bought in some way, it is also more fair to give the bitcoin community a chance to "choose" who should take them over, rather than simply coming out of nowhere and doing it. The important thing is to prevent a situation where a malicious actor eats bitcoin and then copies our features.
Also donkeypong mentioned if such an attack was to be launched, a better strategy would be to clone BTS and 100% sharedrop all current BTS holders, then announce the attack. This would keep the current BTS community out of direct contact with it and avoid the negative risk associated with failure, but keep the positive upside of success. This is a much better idea and I wish I'd thought of that from the beginning.