I'm right eye dominant but not overly strong dominance. I've had similar issues. What I found was that if i hold my head pretty much straight up and down I'll hit left. If I cant my head on an angle equal to the cant of my bow, it goes away.
Basically, what is happening is with my head straight up and down, the arrow is about directly under my right eye. Only problem is, when looking towards the target, I'm getting input from both eyes and its as if I'm seeing from a point between my eyes if that makes sense. Basically, both eyes are providing input. When I tilt my head to match the bow tilt (probably a good 20-30 degrees) the arrow nock is closer to being between my eyes than under my right eye and everything works.
No need though to concern yourself with the details, just try tilting your head and see what happens.