I used to have the same problem, and I found that changing the strike plate material to something softer helped quite a bit. I went from a calf hair strike plate to the Martin rest material. I also used the same material for the arrow rest.
If you tend to collapse at the shot, that is, letting your string arm move forward, you will hit left. When I hit my anchors I hold for a couple of seconds and let my bow arm settle down, and pull through the shot. Make sure you are using your back muscles!