Let me start by saying that you are a strong skier. There is a lot of good stuff happening in your skiing. Here are a few thoughts based on what I see.
Up movement. Yes, there is a bit of an up movement happening as you move across the skis. Instead of trying to extend and push your upper body into the turn, focus on flexing and releasing the outside ski at the end of the turn. Your goal is to evenly exchange length between legs. As the old outside ski gets shorter, the other leg should be getting longer.
You ask about bringing the upper body closer to the ski slope. You also ask about "shifting" the upper body. I get the impression from these questions, and what I see happening in your skiing that you are trying to generate your turns by moving to the inside. Instead, I would suggest thinking about letting your skis travel around the arc to the outside. It is far more efficient to let your feet move rather than throwing around your upper body.
There is one more thing I noticed, especially in your short turns, that I think will help you greatly, and I believe is related to the other things I've mentioned. In the videos, you are "floating" past the top half of your turns. If you watch the short turns video, you can see that there is no engagement with the snow until the skis are across the fall line. Even in the other videos, there is very little engagement at the top of the turn. Part of it is a result of your up movement. At the top of the up movement, there is no weight on your skis, and you end up pivoting through the top of your turns.
If I were you, I would find some easy groomed terrain, and practice Railroad Tracks. Start out slow standing over your feet, and focus on tipping your skis from the ankles only. As the skis tip on edge, the sidecut will do its thing and cause some gentle turning to happen. As you gain comfort, let your speed build a little bit, and continue to tip the skis further onto edge, starting with the ankles, then by tipping the knees as well. Be patient and let the skis move under you rather than moving your upper body across the skis.
At low speeds, attempting to move your body to the inside of the turn won't work. You will fall over. So in order to be successful, you need to be tipping from the ground up.
As for the top of the turn, it is impossible to do Railroad Tracks without engaging the top of the turn. Make sure you are actually doing good Railroad Tracks. Look at your tracks in the snow. They should leave very fine, but well defined arcs in the snow. To help you focus on the top of the turn, pay attention to what is happening immediately before, during, and after the transition. Before, you will be on the two uphill edges. During, your skis will be flat, which means all 4 edges are touching the snow. After, you will be on the two downhill edges as the skis start to turn towards the fall line. Think to yourself, 2, 4, 2 as you pass through the transition.
With regard to the up move, if you focus on tipping from the ground up, and engaging the skis at the top of the turn, I suspect you will find the up movement disappears.