mainly I need to shift my balance to my left foot completely instead of just partially
Don't get ahead of yourself. Lets start from the beginning.
First, you need to complete a weight transfer for your backswing before you even consider impact and follow through. What is happening is you aren't shifting your weight enough to begin with, so there is no need for your weight to shift coming through, which is why it looks like your hanging back coming through it.
Without swaying, make sure you are getting your weight over your right foot on the backswing, feeling it more in your hips than foot. That will cause you to force your body to come through the ball, as you will have no choice if you want to make impact.
I would like to raise my follow-thru to around my neck area instead of down by my shoulders.
No you don't. People would kill for that position. The reason you are hooking it is because your weight is staying back, causing the natural bottom of your arc to be behind the ball. Working on your weight transfer without worrying about this will even everything out in the end.