First off, if your thumbnail is that hooked I'd recommend getting used to keeping it as short as you practically can. You'd be surprised how short you can go and still have an effective nail.
But for the rasgueados you don't need to anchor the nail on the sixth string. You can absolutely have the flesh of your thumb on the sixth string, since the rasgueado position is completely separate from the position you want in order to play a note with your thumb. The only trick is to spend some time practicing the transition from rasgueado thumb to playing thumb. This is one of those things that players sometimes neglect to practice because it seems like it should be easy. But like anything else, a bit of practice is almost always really helpful.
Give it a try with just the flesh of the thumb and let me know how it goes!