I hate to throw this in, but I'm becoming known for this tid-bit. Instinctive is merely something you have practiced enough that you can do it without thinking.
I am left eye dominant and shoot right hand. Many say you can change your dominant eye with practice and exercise by forcing your weak eye to take over. As often as I think of it I make my right eye do the work -- it seems that it does shift dominance, especially if you are aware of it.
When shooting, I occasionally squint my left eye to remind my right eye to take over. Work on it and your right eye will strengthen and soon your sight picture will straighten up. Takes lots of practice. On the other hand, you can get used to your sight picture with LE dominant and just practice until you are hitting what you want.
Remember, trad shooting, especially the instinctive style, is about you, the bow and the arrow becoming a working unit -- that takes a lot of practice.
How many years did it take you to teach your muscles how to throw a ball in the general area you were aiming. With a bow you are aiming at a pretty small spot. Takes a while to make your eyes, muscles and mind (distance) work together in an instant.
However, if you are not confident your bow is tuned right, it could be an arrow spine problem.