Each time I intentionally do a laterally shift will result in low push draw (or mishit), if i just push from the top with my all my body parts follow ( i feel the hip goes laterally first but not as doing a hip slip independently first), the shot is good. I am unable to do the take out the slack move, but I hope it's already done as you said hand control pivot?
Taking out the slack move can be done by pushing up plane with the right hand during the down swing transition while the pivot pulls the left arm. It is a simple move and does not require a hip slide. Works every time.
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