That you have to close your left eye indicates the extent of your left eye dominance. Were I starting fresh, as I am also left eye dominant, I would try a left handed bow.
My dominance is enough that I have to think about it to SEE through my right in order to aim. Otherwise, I just naturally use my left, or both. In a hunting situation, you don't have time for those shenanigans. I have shot right-handed for so many years that whatever my aiming system is (I am afraid to analyze it!!) has adapted to my eyes' condition.
If you have to squint or close the offside eye, you are sufficiently handicapped so as to seriously consider a lefty (or "correct", as a minority here would say) bow. Lucky you, you have a chance to start out correctly.
The other option wold be to buy an old double shelf Cub or Grizzly from the 1950s, and switch hit at will.
Killdeer