Along the lines of the drill being done, I'd ask him to ski the same run keeping the shoulders constantly faced down hill.
I can see "those" in the (let's call it) "carving" camp, going "OMG - you're permanently ruining this skier". My second reaction ( ) was "It's just a drill (take a breath). It's just a drill". So the kid is a pretty solid unit and more solid than we'd normally expect for a 6 yo. The only separation he's getting is shoulder driven, but he's also got a fair amount of power turning his feet. This is normal out-in development for a child. My preference would be to do physical development off skis and live with the performance hit of lack of separation during parallel skiing for now. He's due to grow out of this soon enough.
So I'm with Epic, except that I'd start with looking at how he skis "normally" (i.e. not doing this drill). He may already know how to let the skis turn him.
So good to see that many of the instructors are taking into account the neuro-muscular development of the child. First a couple of general things for teaching children of this age.
Never use a drill as such with this age child. Hide the drill in a game of some sort. The drill will soon be forgotten and never repeated. A fun game will be remembered and repeated and better yet shared with others. If you can keep it so simple that a six year old can teach the game to friends and family I can guarantee a successful outcome from the lesson.
One thing at a time. Eliminate the word ‘and’ from your lessons with children this young. They are just not ready to hold two concepts in their minds at the same time let alone perform them.
Now, this child in particular.
You referred to him as a level 9. He isn’t. He is a level 6-7 that skis very defensively. I will assume that he is called a level 9 and skis defensively because of the steepness of the terrain that he can ski down. He shouldn’t be on that terrain, not until he loses the back seat push the ski defensiveness and the stem entry to his turns.
Start by de-emphasizing the idea of ‘turning’. When skiing we don’t ‘make turns’ we go there and then go over there or go back and forth on the hill in curves, emphasize the ‘go’ part of this.
Tell him to point his toes where he wants to go. This will get him to learn to use his feet and legs to guide the skis instead of using his whole body. Do this on very gentle terrain and encourage him to go fast. After pointing his toes for a while put a black sticker on his left ski and a white sticker on his right ski. Tell him to go that way (point to his right) all he has to do is to point his white toes that way and to go the other way (point to his left) all he has to do is point his black toes that way. This will get him leading into the turn with his new inside ski. These things will also help him center himself over his skis.
On very gentle terrain have him walk or run through very big arcs (This is thousand steps for kids), you might even want to start with figure eights on flat terrain. These things will get him centered over his feet.
Personally, I would recommend dropping the idea of short radius turns. All that will do is re-enforce his back seat push the ski style of skiing. Once he learns to work the ski a little his small size and the very small side-cut of his skis will produce very short turns when they are needed.
This is a whole seasons worth of things for a child of this age but it will produce a skier who is well centered and capable of skiing the whole mountain.
PS. Forgot one very important thing. Teach him to skate on his skis and do a lot of it. Again this will get him centered over the skis.
Here's two screen captures that are pretty representative of how the young lad skis through the clip. This looks like pretty decent fore/aft balance to me:
When he extends, he comes straight up because he's opening his hip joint more than knees & ankles, but I still don't see him sitting back. I really like the way he comes to a stop leaning way forward on his poles -- the way they stop is a cue to the way they ski, and the ones who come sliding in on their tails are the ones that need fore/aft work.
This terrain is well within his comfort range and ability, and I would continue in this environment, adding some speed with good runouts, and playing in steeper terrain as well.
Going back to gentler terrain for technical training is not something I would be doing with this six-year-old. I would hate to see that smile get lost in drill training.