first post here... allow me to jump right in on a topic i've grappled with considerably...
i am left-eye dominant and a RH shooter - i started that way before i knew anything about eye dominance so it was never an issue for me... then i started reading about eye dominance and got all concerned that perhaps i'll never get very good at this game unless i switch to left-handed...
well, by no means am i any kind of olympic-accuracy shooter, but at the distances i'm willing to shoot, i can put an arrow plenty well into the kill zone...
i am PURELY an instinctive shooter - i don't even see the arrow until i let it loose... i flirted with closing and squinting my left eye and i could see the potential for better accuracy, but what i noticed straight off that when i force my right eye to be dominant (by shutting the left eye) i REALLY see the arrow - and it's REALLY hard to avoid the temptation, darn near impossible for me, to sight down the arrow and "aim" it... when i have both eyes open, the target is the prominent feature in my vision - when i focus with my dominant eye, the arrow becomes the prominent feature and it's 90% of what i see because it's right there under the eye - i can't NOT look at it! which i guess is the point of having the dominant eye over the arrow, but i don't like that because again, i prefer to shoot purely instinctively - and when i have both eyes open all i see is the target and i'm not even in the least bit aware of the arrow...
so short story is that i don't buy the ballyhoo about "you'll never get accurate with cross-dominance"... i won't argue that perhaps my groups would tighten up some if i matched eye to arm, but i'm not a target shooter, i don't compete - i can get done what i want to get done with a left eye and RH bow, confidently, and it keeps me "purely instinctive"... i see no reason to switch and i FIRMLY believe that our brains are more than capable of compensating and overcoming the cross-dominance issue... i mean, if you're an instinctive shooter, you're basically relying on your brain to "do the math." i think it's kind of dismissive of the brain's potential to assume that it can't adjust for 2-3" distance eye-to-eye...
in the end, i say go with what you feels right to you and don't worry about eye dominance - trust your brain figure it out and it will (assuming you shoot instinctively, of course...) but i guess if you're looking to be as accurate as possible, it sounds like more than a few folks report increased accuracy by switching... but for all PRACTICAL purposes, at least in my case, any improvement in accuracy doesn't really translate into enough difference to make it worth a switch... i'm gettin' the job done either way...
p.s. this might be a bit speculative, but you know how you have good days and bad days shooting? surely everyone here has noticed how when your mind is in the wrong frame, you can't put an arrow in the circle to save your life...i think the same factor is at play in being concerned about eye dominance - at least i've seen this in myself... when i was grappling with the eye dominance issue, my shooting got worse - my mind was more concerned with dominance and "should i switch?" and "maybe i'm doing this wrong?" and "gosh i really want to be the best shooter i can be what should i do? is eye dominance important? maybe? maybe not?" when i just said "screw it, i'm shooting RH" i didn't have any more problems... so if you're gonna' worry about eye dominance, i guess it might "ease your mind" to switch... and if you can just let it go and not make it an issue, the brain will be freed up to learn how to shoot quite well cross-dominantly... KEEP YOUR MIND FREE OF DISTRACTIONS, FOCUS ON THE TARGET AND IT'LL ALL WORK OUT, that's what i believe...
if christy brown could learn to paint and write with just his left foot, i'm purty sure the brain of a healthy individual with four working limbs and decent vision can figure out how to shoot accurately cross-dominantly... relax, trust it and let it do its work...
i guess what i'm trying to say (and i'm sure after all this babbling and rambling i've done, you wish i had said it with several fewer paragraphs!) is that if you make it an issue, it'll be an issue... if you don't, it won't... (i'm talking with respect to INSTINCTIVE shooting ONLY... i can't say anything about other methods as i have no experience with them...)