Other than the spine issues already mentioned, a miss to the right for a RH shooter is most commonly caused by a pluck. But you are definitely not plucking if you are grouping well.
If you want to shoot to the left, I can give you about 12 errors you can make, any of which would cause you to miss to the left (DAMHIK). At one point, I would give almost anything if I could start missing to the right.
Sometimes a right miss can be caused by modern bowyers cutting the shelf in past center-shot. This can easily be cured by building out the shelf with leather or some other material. As you look down the arrow, you should see the tip of the arrow just to the left of the bowstring.
The bottom line is, I think you've got an easier problem to solve than if you were hitting to the left.