Congradulations! you must have been shaking with glee! Since he was kind enough to get into a carrier, is he kind enough to be given a home? He sounds like he might be..
Funny, my friend jan has a "Kirby" whose a twistie cat and on top of that has a back leg that every now and then pops out. The 1st time she noticed it, it was because he wasn't moving , hiding and not eating. But at the vets, it had popped back in on the ride there- vet knew immediatly what the problem was. So Kirby's hip pops out and Kirby's hip pops in, this is part of the legacy of these Twistie cat breeders!
But none-the-less! thank god you got him! Can you pat him?