I'm right dominant and am learning to shoot lefty because of a bad shoulder. I've learned that I have to lean my head and cant the bow quite a bit more than I did when shooting righty. Reason is to get the nock end of the arrow directly under my right eye. Fred Bear was right eye dominant and shot lefty as well. After wondering for all those years why Fred Bear used such a heavy cant and head tilt, it suddenly made sense.

Anyway, accurate shooting at longer distances can be done, it's just not as easy as matching your shooting side to your dominant eye.