The CLR doesn't move, the board is not necessarily supposed to move aft for the purposes of gybing. The board being angled with respect to the hull means that lift can be made to weather while the hull is travelling straight forward to make less leeway. Some boats were built with toe in in the trunks of the boards. With that method you have to raise the windward board. As said above nothing fancier than slop built a specific way into the board is needed. Pictures make it easier to understand.
http://www.philsfoils.com/designTips.html#gybingheadJohn
