This is a good reason to shoot TRUE INSTINCTIVE.
Easy to teach in person but difficult to teach with just words.
I myself don't have a dominant eye but luckily, my dad thought me to shoot when I was 6 years old.
It's like throwing a ball or a dart, just look at where you want to hit, and hit it.
DON'T LOOK AT THE ARROW!
A good way to start is "Blind Bailing"
Stand close, like 5 yards and get a good stance, get your bow ready to pull up while its still down and crosswise like carrying a suitcase in front of you.
Now look intently at a spot you want the arrow to go, visualize it hitting that spot, close your eyes and bring the bow up, draw, anchor and shoot.
Now open your eyes and see what happened.
Now for the time being, you adjust your feet according to whitch way you missed.
It will be very fun when your brain figures out what you are doing.
Believe you can do it and stick with it for a while.
When you start hitting where you want, move back a bit and have have it.
If you master this, then start messing with changing your stance and even twisting in the opposite direction.
Good luck and I wish I could work with you face to face. I have thought many people how to do that.