If you look at your video you will notice that you ski fairly straight and then very quickly make a very tight turn with small radius and then ski back the other way. You are rushing your skis through the fall line, spending as little time with your skis pointing down the fall line as possible. What you should be doing in order to carve is very gradually tip your skis, and patiently wait for them to come around. You will pick up more speed when you spend more time in the fall line, but because your edge-locked turning skis have such a good grip, you can keep turning right around until your are skiing uphill. Skiing uphill is a very good way to slow down, when you have the room on an uncrowded slope to do so (not when you are joining another trail and skiing up it in a blind spot). So start your turn sooner so you can gradually tip onto the edge and keep tipping to keep making the turn tighter and tighter, then gradually untip until you're gradually tipping the other way; make S turns not Z turns. Make the ride down the hill a constant ski tipping exercise, tipping the skis one way and steadily increasing the tipping angle, until you are almost going uphill, then start to decrease the edge angle and loosen the turn, decrease the tipping angle all the way through flat and right into the next turn and repeat. One turn ends gradually as the next one starts gradually. Don't rush to turn at the fall line, just keep steadily turning when you get to it.
You need to get a little angulation/counter balancing going on, so that you can dig those edges in, not push them out. Here's a little drill for that. Grab both your ski poles and hold them together with one hand near the grips and the other near the baskets. Hold the poles horizontally in front of you so they line up visually with the horizon. Ski down the slope, making turns while keeping the poles lined up horizontally (with the horizon).
You need to get a little upper/lower body separation going on. A fun little drill that will help with that is the picture frame drill. Grab your ski poles near the baskets and hold them up in front of you vertically, so they act like the sides of a picture frame. Frame the picture of the bottom of the run (with the lodge and parking lot or what have you). Now ski down, keeping the picture in the frame.
You can try to add elements of the picture drill to the horizontal pole drill. (keep shoulders and hips level while you keep facing downhill).
Try to dig those edges in, not push them out. In fact you don't need to push, you just need to resist the push that will come when the skis turn and you get pushed against them by inertia. Carving edge-locked turns is about keeping those edges locked down; pushing tends to work against that (though you may have to push like a SOaB when you dial up a hard turn in a compression).
If you are having trouble tipping the skis, just concentrate on gradually tipping and lifting the inside ski more and more while allowing your body to make adjustments to the changing balance.
Let your weight come onto the outside ski; it does most of the work. Later you can worry about parallel shins and keeping just enough weight on the inside ski to keep it arcing too.