This video was interesting. As someone who battles a perpetual stem and push I am curious as to how trying the experiment he had his trainers do would work for me. I tend to get stuck kind of in a squat. Exaggerating that and the opposite (stand up) is an interesting idea that goes along with Deb Amstrong's latest videos about moving forward at the transition, which is something I was just starting to play with last season. I've heard the "don't move up and down" thing so often that I've kind of had it beaten into my head, yet, it might be that exaggerating it at least temporarily or as a warmup will ultimately get me to find that feeling of releasing at the right time that will eliminate the stem (as he said it did for the instructors in the video.) They then find the balance and rhythm and drop the exaggerated move.
The section in that vid labeled "Hidden in plain sight" - (from the cued to about 14:10) seemed most relevant to the other poster. (Adding vid to a post allows a start point but not an end point.)
In terms of the stem... that's not one I've had to struggle much with in carving. (Not to worry, plenty of other issues that more than make up for it! ) However transitions are something I've been working on for the last few seasons, particularly in carving where the aim is to have no pivoting of the ski. Can only write about what has helped me (which may or may not be applicable to others) and that's using the forces from the previous turn to move into the new. Aiming to bias balance progressively to the outside as the old turn completes (skis coming back to me, angulation increasing, CoM already largely redirected across the hill but still moving partly down, absorbing to manage the pressure). My take is that flexing alone, without the CoM on the verge of, or already heading across the skis, simply makes for a low crouch and needing to do something wacky with the old inside ski - like a push-off or a stem.
I'm sure I'm about to get lots of advice for doing it better. Or how that's completely wrong. Where I'm up to. Work in progress.