For the last few years I have been a pain in the butt to many clinic leaders because every time that they tell the group to move their cm into the turn I have asked them just how to move it. They don't like the question because they don't have an answer. They can't tell me which muscles to use to push the cm across the skis to the other side because in a skiing situation there are no muscles that will do this task. Some start to tell me that extending the, at that moment. uphill leg will move the cm across. I point out that untill the edge has changed extention of that leg will act to move the cm away from the direction that they want to move in. These people watch a skier and see that the cm moves from one side of the feet to the other and come to the conclusion that we have to 'move the cm across the skis into the new turn'. This is such an easy statement to make that for years it was the mantra of how to teach skiing and led to a lot of banking and rotation into the new turn.That was OK though because it gave the instructor/clinic leader some 'errors' to 'correct'.
Here's my take on what's going on.
First, my cm is already moving along at a pretty good clip, 10 to 15 mph when I'm skiing slowly and 20 to 45 mph for most of my skiing. I'm using the force I generate with my skis to direct my cm where I want it to go. The greater the force I apply to the cm the more I can change the path it is traveling along (the tighter the arc i am following). Now if I lessen the force on the cm then it will follow a path of less arc and if i remove the force completely then the cm will move in a straight line. By relaxing or actively shortening the outside leg during the last part of a turn I am lessening the force applied to the cm so that it will follow a larger arc yet my feet are still being carried along the arc created by the carving ski. The cm and the feet are now moving along very different paths, paths that will cross and produce gross edge change. I can further control the crossing of the feet and cm by manipulation of the edge angle of the skis. Less edge means less force to the cm so that the cm follows a straighter path and if I suddenly flatten the ski the cm will go balistic and follow a straight path untill I begin to apply force to it again. Since most of the force is being transmitted through the long strong outside leg then I can produce the greatest effect by focusing on flattening that foot when I come to the point I want to transition from one turn to another. That is a very long way of saying I allow my cm to cross the path my feet are following rather than continuing to direct it along another path. This is also very akin to what you are describing as cross-under, I just try to avoid the use of cross-over, cross-under because the two should be blended smoothly together in upper level skiing.
More tomorrow in resopnse to your question about the effectiveness of inside foot use to create and shape turns.
PS Was yours the article on inclination/ extention through the top of the turn and allowing greater creation of angles through the bottom of the turn? That was a great article and happened to dove tail with what I was babbling about last season in realtion to upper level skiing.