Just to clarify, when I speak of eye dominance and everything I've been taught and read and experienced, is with both eyes open. Depth perception is critical having both eyes open unless you sight aim...including point of aim (without sights using your arrow to sight down). But even these methods are better if you can adjust to shooting both eyes open.
Rezeen, look back at what all these guys are saying. All the left eye dominant guys shoot much better when changing their bow hand. Don't trouble yourself more than you need to. Go with physics, science and with what just plain works. Don't fight your body.
Fred Bear and Glenn St. Charles...two of my favorite guys ever. Met them both. Icons, hero's you name it. But if they preached to anyone that eye dominance does not matter in archery, they made an error in judgement. Absolutely no disrespect, everybody is wrong at one point or another. I'm not making this stuff up, research it for yourselves.