Hello Paul,
I am a natural LH shooter who was also left-eye dominant for at least the first 40 years of my life. By then things were changing and it got so my left eye could no longer even be corrected to make its vision equal to my right (started wearing glasses when I was ~30). Sometime along in there my right eye took over dominance (I don't know how long it was before I realized it).
A few years ago I decided to learn to shoot RH. When I was a kid, I could always hit a ball well from both sides of the plate so I figured why not a bow too?
I had never once in my life even tried to draw a bow RH. I don't know if I went about it by an "accepted" method, but I decided form was the most important thing to work on first. So I borrowed an old 25# bow and just practiced drawing it for about a month - never shooting a single arrow; just concentrating on my draw and anchor (sometimes with an arrow on the string, sometimes not).
Then I purchased a used 40# Black Bear and continued to just draw and anchor for about another 6 weeks - never shooting an arrow (I continued to shoot LH throughout the process).
From there I moved up to a bow around 55# and started shooting. Even with the first arrow, it didn't seem "odd" to be drawing and releasing an arrow RH. For me at least, I think it was a benefit not worrying about shooting and accuracy while I was building form, toning RH muscles, and building muscle memory (and hopefully good habits).
I still shoot LH too, which is bad for the bow inventory!
However, I feel a little more "in control" when I am shooting RH.
It also came in handy late last summer when I injured my right elbow. It gave me a lot of pain as my bow arm (LH) but none at all as my drawing hand. So, it has been a real advantage to be able to rest it and let it heal (which it about is) while still being able to enjoy shooting RH.
Good luck to you with your switch, stick with it!
Take Care,
Tom