The direction of the forward cast also determines the direction of the haul.
For example, when the casting arm is pulling the rod down, then the hauling hand has to go down faster and farther to compensate for the lowering of the rod during the forward cast.
I would experiment and see if you can cast more in a straight back and forth direction so the haul does not have to go down as much.
Take a look at the 3 major arm styes of casting in the pdf below. If you normally use the elbow forward style (#1) below, this drops the casting elbow and the rod and the hauling hand will go down on the forward cast.
Consider the elbow up and to the side style (#2) of casting that does not drop the casting arm as much.