Hi Slicepong,
Yes this backswing is really important to get right I feel for most players. Definitely tey to use the body rotation and shoulder as well as coiling the bat back, as you said it soeeds things up and gets you into a good position quicker. One very important part of the backswing is trying to stay relaxed with all the body parts moving back, if you get tense it means your fighting against your body and not working with it, so really focus on being loose and relaxed in the backswing, especially with the arm and shoulder.
