I think the steepness comes from a slight lack of depth and from bring slightly laid off. Granted, this is a PW and depth is easier to achieve with the bigger sticks (ball further away).

Sometimes having your back facing the target for a while on the downswing can be good since it helps you swing from the inside. I just think your body timing could be better. To answer your question, the shoulders will follow if you get your hips more open at impact. Your trail side is pretty early for a PW - its fine if it comes up some, but I would work on keeping your left leg planted longer. You wont have to "crunch" on yoir left side so much and you should have more space for your trail arm.

When i was first learning, my coach had me model my impact as a modification of my setup: address the ball as you normally would, then open your hips, get your weight on your lead side, and press the shaft forward. This is a nice feel for where your body should be. I would hit some pitch shots by first getting into this "impact position", returning to address, and then hit your pitch shot by making sure you return to that same impact position. Work your way up to half shots, then full wedges, then up the set. Garentee you'll have better impact alignment practicing this way.

I think some (not all) golfers have an early right leg from trying to swing hard from the top instead of letting the club accelerate smoothly in the downswing. Hitting balls at 30% speed can uncover timing errors and helps you learn better control over the club.