You mentioned Pushing your knees forward, and I think that may be the key. Instead of pushing knees forward, you could try to think about pulling them back. This will help with the vertical shin angle Evolve mentioned. Right now, you use tons of lower back, to over arch and pull yourself into an upright position, then squat the weight up with your quads.
Look at the 40-41 second mark of your video. As you go Up Your knees are "forward" and you have to pull the bar way out and in front, to get around them. If you look close, you can see daylight between the bar and your legs! This is not good.
If you look at 56-57 seconds, as you lower the bar, you can see your knees go backward to get out of the way. Your shins are vertcal, and the bar goes straight, staying close to your legs. This is good.
The width of your stance, and how far you turn your toes out are going to vary a lot from person to person. But with your feet so close, and your toes so straight, it looks like you can't get close to the bar. It's out in front of you. Maybe If you open up a little, you can get the bar closer to you at the start.
I just now learned about "waiter's bows." Double Aragorn shout out! You should try some, outside of the gym, 3 times a day for a week or so. Focus on hinging, and really loading up your hamstrings. Also pay special special close attention to the hand that is on your lower back. Your lower back should not "move" or "arch more." It should holds its position, straight, like a steel bar as Your hips drive forward.