In hitting, the left hand is the "fulcrum", whereas the right is the "force" (and the club is the "weight")-class III Lever, in which the "fulcrum" needs to be pushed against (as well) in order for the "force" to be applied.
In hitting, the right hand can be the "fulcrum", whereas the left be the "force" (and the club is the "weight")-class I Lever, in which the "fulcrum (the right hand)" needs to be pushed against (as well) in order for the "force (the left hand)" to be applied.
In either case, the left hand/side needs to "push" (while being pulled/draged by the pivot).
In Hitting, we are accelerating the Primary Lever Assembly which has a Form III lever with the Fulcrum at the Left Shoulder, not the left hand. When the Fulcrum is in the Left Wrist the Weight is now in the Clubhead an additiional Form III lever used normally in Swinging; accelerating the Secondary Lever Assembly. Reference 2-L, 6-A-2, and 6-A-3 and let me know how your application fits into TGM.