I am the same way...right handed but left eye dominant. I shoot right handed, and I think I simply turn my hend into the string a bit more than average (placing my left eye over the string more). Either way, the brain will figure it out and compensate for it, It will just take time, like anything.
I can shoot left handed with a lighter weight bow, and actually shoot it better at short distances. But, it does not feel natural to me, and I cannot pull near as much wieght without loosing my form.
I agree with others that say let him shoot what feels best. He will have to practice either way, so it really won't be an issue.
The only time I found it to be an issues was sooting with a peep site (compound bow) or shooting with a shot gun. I cannot hit anything with the shot gun until I close my left eye. It takes a few misses until I remember!!
AkBillyBow