[ThinkingPlus]

I would expect that if the club face moves a little over 2 cm while in contact with the ball, then the center of the ball moves that much as well. Think of it this way. At initial contact, the center of the ball is 1/2 ball diameter from the club face. At the end of the contact period, ~ 500e-6 seconds later, the center of the ball is once again (approximately) 1/2 ball diameter from the club face. However, in the intervening time the club face has translated along the swing path ~ 2 cm. Therefore during that same time, the center of the ball has translated the same 2 cm.

I have not looked into this sort of thing in that much detail, but to first order my description above seems reasonable. It also may not be entirely pertinent to your discussion.