. . . as far as my right dominant, left eye dominant... what is best strategy for this in terms of aiming?
I don't think it's possible to be certain which is the "best" strategy for you to deal with the problem. No one here can see your current stance and shot, or know your purpose. What I *can* advise is to (1) figure out what problem - if any - your cross-dominance is causing you, and (2) consider one of the several strategies for dealing with it.
I advised earlier to shoot a group as you currently do, no changes. Then close your left eye and shoot a second group. If cross-dominance is causing you an issue, you'll see a difference.
As for dealing with it, you can:
1) Train to be right-eye dominant (they say it can be done, but you may not be aware if you revert at the worst possible time)
2) Close your left eye, align sights with right eye. (may lose depth perception, peripheral vision. *May* be important to you)
3) Use both eyes, align sights with left eye (stance a bit awkward)
4) Change nothing except adjust your hold for the variance you saw (tricky as distances and sight radius etc change)
I am right-handed, right eye dominant, but have an issue in my right eye causing multiple and blurry images of the iron sights in that eye's image. Until that is fixed, I've chosen to shoot right eye closed, sights aligned with left eye. YMMV.