Please do not change the pots. It is not necessary because if you have a look at the red mini controls hud (RCTRL-ENTER] you will see that the diamond will follow the smallest inputs from you cyclic. It s not really a dead zone. I'm almost sure they programmed it as well to behave the stick like a real one.
In real life a chopper cyclic has the same issue as well and makes it easy to "stir in a pan of soup" which you HAVE to do to keep the Huey on one spot.
But, honestly speaking, my first reaction was the same like yours. :) Until my friend, who is flying choppers for real, came over and fly the huey with 2 fingers in his nose. He was very impressed over the correctness of the stick.
As a guide for starting hoovering. Trim your cyclic just in the left under quadrant (mini hud) and slowly start raising the collective. During that proces give a little left pedal pressure. Hold your Cougar grip with 2 fingers.
Keep practising, practising, practising. No need t change the pots until they are becoming spiky.
However, Microsoft made a vey good quality joystick, far better then a logitech G940.
Good luck.