@AdamCord, thank you for responding to my query about the rest of the GUT approach. I too, look forward to the unabridged version. Regarding what you wrote above, on the Reach, I think you are spot on in your analysis. While I believe in the counter and found that it had a significant effect on my skiing, I had never considered the effect it has on extending the reach. So I stood as you suggested and reached with and without countering and the difference in the amount of reach is significant. Great example, great explanation. I also agree with most, just not all of your section on the Pull. But I will leave that alone.
With regard to the counter and it's relation to the turn though, I think that something is being overlooked by skiers that believe it is either not related or would have little benefit. If you compare waterskiing to snow skiing, you will find that correlation. A snow skier knows that the only way to turn effectively is with the lower body. Although it is counter intuitive, even in snow skiing, if you want to turn to the left, the torso stays down the fall line while the hips twist beneath the torso. And if you want to turn even more agressively, the feet, ankles and knees all press into the hill to roll the ski on edge as much as possible.
Applied to waterskiing, when you open the chest or twist slightly away from your desired direction of travel, the result is that you are telling your body that the only way to make the turn from that position is to twist the lower body and edge the ski just like a snow skier as opposed to simply falling with your entire body staying straight as in the "old style" waterskiing. Edge to turn, don't fall to turn.
Equally as important is that the counter combined with the reach you described when it is in an upward motion, automatically levels the shoulders entering the apex which prevents the upper body from falling toward the wake, further enhancing the movement of the lower body. The hips will instinctively drop to edge the ski even further as the skier resists to maintain his postition and keep the torso upright. The end result is those terrific pics of guys like Nate Smith or Marcus Brown, virtually sitting on water at the completion of the turn with the ski dramatcially rolled on edge. Although I do not have a clue regarding the bio mechanics and why turning your torso one direction, enhances the ability for the lower body to turn a ski in the opposite direction, I know it works and the guys who know this best are also great snow skiers like Marcus or Jamie Beauschesne. I may not have described all of this as well as I might have and if there is a snow skier out there who can do a better job please chime in.