Well I'm not exactly sure how the superman pull is supposed to be done but I have an idea. I know you're trying to bring the bar in super close on the 1st Pull but I feel like you're shooting your hips up way too much. You can still keep the bar close without dramatically elevating the hips. I do notice that you start with your hips a little lower than usual, which is fine, and your hips may move up a little sooner that your chest but I feel like it doesn't need to be that significant. When the bar reaches the knee your torso is almost perfectly parallel to the floor.
Try to keep you chest up more on the 1st Pull. Remember, you want the bar to go UP. There is just too much horizontal movement/weight-shift going on on the 1st and 2nd Pull and that's what's making the 3rd pull so difficult causing the bar to crash on you in the bottom. You kind of jump out of frame so it's hard to see the 3rd Pull but I can definitely see the bar crash. Keep that chest up more in the beginning and that should help clean up the rest of the movement. Try to keep the torso more like the DLs in the second video.