Punitive damages. All you need to do is show the other party acted with malice or through fraud. Punitive damages are designed to be a punishment for the bad actor, you can net some nice coin that way if the judge is particularly unhappy with your opponent. Just get try to get in touch with the ACLU to see if they can give any advice before you file, the case law for this stuff is complicated last time I looked into it.
To be perfectly honest, it felt good to write. And that was enough for me.
But... I just talked to an experienced litigation lawyer about this hypothetical, and was told that success really depends on how Twitter handles the notice - how public is it, do your friends and business associates see that you were subjected to a DMCA takedown, etc.
The time, expense and stress is a pretty obvious downside for many if not most.