Notice how Mike Trout stays inside of his rear leg and how calm his upper body is and how little sway there is. Compare that to what you are doing. Try to load up and keep your weight inside your inside your knee. Try to load without the big movement in your upper body, notice how big a kick Trout has but how little sway there is.
https://www.youtube.com/watch?v=lX_dm39fkfw
The other thing I noticed is that you are not hitting the ball far enough out in front of you. See where Trout and cabrera are hitting the ball
An example of the bat throw drill is here.You are very similar to what my son was doing in HS and every time he went to the cage the first thing he did was throw the bat before he started hitting balls, it just got his mind set in extending out through the ball.
https://www.youtube.com/watch?v=ZaD4Rwt38wI
You will see similar action with Miguel Cabrera
https://www.youtube.com/watch?v=SqoRjU0ZXTk
They both load up but don't have the big sway in their swing that you do. Notice how both of them drive to the pitcher with their front shoulder down.