JDK,
I am a newbie getting back into archery after 20+ years so my opinion may be totally worthless or more apropos to your situation.
I'm a LED/RH shooter and have done fine all my life. Guess I learned to adapt. That includes scopes, iron sights, peeps, wing shooting, etc. On guns with open sights I just learned to shut my left eye at the last second and I seem to do fine.
The only thing I find my self shooting 'left eyed' is handguns. If I just bring them up instinctively to aim I always end up shooting left eyed.
Regarding bows, I got mine right before Christmas and already have zero problems attaining hunting level accuracy even to 40 yards, so far. I am using a peep and a Black Gold Ambush Ascent sight. Obviously, I continue to practice from different positions trying to develop a rock solid muscle memory for those times (hopefully!) when the big buck or elk steps out and my heart is going triple time!
I guess it depends on how 'ambi' you feel you are. I play guitar (lots of LH Action going on there!) but still didn't feel comfortable with the idea of trying to learn to shoot a bow left handed. What I'm saying is, IMHO, you'll be just fine with your RH bow.
Just one guys (newbie) opinion...