Impossible to shoot a compound right handed using a peep and sights with a left eye dominance and using that left eye
Exactly!! Thats why myself , and many other right handed shooters with left eye dominance shoot right handed and close our left eye.
Left eye dominant shooters shoot right handed and use their right eyes - their NON dominant eye. Now, when you draw the compound and anchor, that peep is right there for you to use with your right eye.
USE IT
I do , and it works great for me! I just close my left eye like this.
When I shoot my recurve (no sights) , I keep both eyes open , totally different ballgame.
If your telling me that you shoot a right handed compound , with a peep , with both eyes open , while being left eye dominant , I'm telling you that your "left eye dominance" isn't nearly as bad as you think , or nearly as bad as other left eye dominant archers (myself included).
The more I read your reply , the more my head spins.

I think we might be trying to convey the same message?[&:]I dont know , just shoot!