just for fun, look up all of the top shooters in the world.. 90%+ shoot 3 under.. There is a reason for that. It has a lot more to do than eye dominance. I would say a flyer has more to do with release than eye dominance, but that's just my opinion.
A lot of people(me) struggle with split because of them applying too much pressure on one finger or the other. I have always shot split and loved it because it "feels" right. I recently, due to a crazy callous, started shooting 2 under where i just keep my index finger off the string and I like it a lot! smoother release, more consistent, etc.