I am right handed and left eye dominant. I have been reading a bit on this forum and most seem to recommend shooting lefty in this situation. I have been shooting for about a couple years right handed as that is what type of bow I could find. I finally got a good left handed longbow at a reasonable price. I have been shooting for just a week and the switch has been much easier than I anticipated. I have only been out 3 times as a lefty and at first had some release and alignment problems. Today I made some pretty good progress and was shooting dead on straight. I still don't have my range dialed in past about 25 yards but that will come swiftly. Advantages of being able to shoot with both eyes open is quite large. Before I would look at the target arrow knocked and bow in a neutral position. Decide how far the target was, then begin the draw, close left eye, aim, and release...
Today I was able to gauge the distance as I drew the bow, come to anchor and then just shoot. Much quicker obviously. Now I just have to train my left hand to not fumble the arrow on the journey from quiver to bow. Thanks for the advice and videos guys, I have learned a lot lurking here.