Looking at all the responses given, I would agree with a majority of them. Including the good athletic skiing.
As far as being in front or getting in front, Try unfolding your knee and hip (especially during the shaping or apex of the turn) A lot of times instructors call this "getting taller" (including myself) but as I learn more about how we relate information to our students it really doesn't make a lot of sense. I've been trying to come up with other ways to communicate this. . Try thinking about opening your ankle more (don't loose the front of your boot) and as you open your ankle try to open your knee joint and hip joint even more than your ankle.. To the point where your femur is pointed right at your toe piece. When you are in the apex of your turn, This is where this extension should be longest. As you enter the finish part of the turn, don't be in such a hurry to lose all that extension. Don't brace against it either. This is where lightening or relaxing of that old outside leg will release your edges. If you do this progressively while starting to progressively extending your new out side ski you will be able to keep moving in front of your feet and thus stay forward.
Look at every picture and image that all the posters have extracted from your video and look at the outside leg.. In every case, even where it is the most extended, the femur is pointed at the front of the ski or even past the tip of the ski. This is your hips and most certainly your COM being well behind the ball, arch or even the heel of your foot. You are using all muscle to fight the forces being created by your moving through the turn. At high speed, this pressure is magnified. (including bumps) and thus your burning quads.
Getting all your COM over your feet will allow you to use much more bone structure to withstand all that pressure.