I can't make it out on either of your videos, but what is your lower back doing at the bottom of your squats? Is is staying in extension, or rounding? You already noticed your knees coming in. It may be time to move your stance back in and see how it feels.
You have a tendency to shift on to your quads about halfway up on the ascent. Just keep driving with the hips and the rest will take care of itself. That will also help with the bar path and speed through the middle.