You might need to slow down until you get the hang of it like I said, then gradually speed back up to normal if you can. Don't get caught up in trying to go fast for the sake of ball speed, this might be why you are twisting because you are trying to catch the ball up to your feet. Slow down and stay lower and see if you aren't in a better position and more consistent. If so I can give you ways to get your ball speed back up besides running to the line.
Agreed, I believe the reason your body twists, your slide foot turns to the right, as well as the rearing up at the line all have to do with your speed. You are too quick to the line right now and it is causing you to pull the ball all the way through the swing. This contorts the body and forces you to bind up in order to create speed.
Try to relax and slow down as CoachJim mentioned in order to get your body into a better position at the line. Once you can stay stable (and down) at release, then you can begin to add speed. Just remember speed is added more in the power step than in the arm so use a strong push into a solid position at the line and your speed will be there, without all the jerky motions.