Hi Alex,
as far as I know, it's not really important whether you're right or left handed.
What makes the big difference is your eyes!
As you say, you've got a dominant right eye, in fact this is something you can check easily.
When shooting, it's important to get the string as close as posssible in front of your dominant eye, which helps you keep the right direction.
So if your right eye is really the dominant one, you're supposed to shoot a right handed bow, because otherwise your string is in front of the wrong eye - no matter, whether you're right- or left handed...

Again i´m on Grizzlys side

Do what's natural for you, with the "instictive shooting" it does not really matter what eye dominance you have , but if you force your body to do something that does not feel natural you will  find it very hard to get a good hand-eye coordination.

me, for instance, i hold the bow in my left hand, but with the slingshot i use the right one, left just does not feel good.

@alex321: if the bows are NOT built, maybe you can cancel them or make the bowyer to build them for the other side side ..

other than that: there is always the BIETE section were you can sell them