My advice isn't worth much, but I'll chime in.
I'm cross-eye dominant (right-handed, left-eye dominant), but am way too stubborn to shoot left-handed. I know I could make the switch, I know others have, I know it's only hard for a while... I know all of that, but I just don't want to. SO shooting right-handed with a left dominant eye means if I was going to aim, I would pretty much have to close my left (i.e. dominant) eye and use my right (non-dominant) eye to aim down the arrow. Tried it some in the beginning and didn't like it.
Shooting instinctive, with both eyes open, on the other hand, seems to work FOR ME. Not to say I'm a great shot or anything like that, but I've become proficient at it. It seems to be the best way FOR ME to keep both eyes open while being cross-eye dominant.
While I am going, let me say something about the analogy we often use to throwing a baseball or shooting a basketball. While I understand what's meant, I've always felt they fall a little short because, unlike throwing a ball, there is something else (a bow) between the shooter and the arrow. Those analogies of throwing baseballs and shooting basketballs would work better, I think, with something like throwing a spear.
What makes more sense to me is comparing instinctive shooting to what a good baseball coach does when he grabs a bat, tosses a ball in the air, and hits a perfect pop fly to the left fielder. And then hits a perfect grounder to second base. And then a line drive to the shortstop. And all the way around the field to every position—including over the fence when he wants to show off. That, in my mind, is closer to what is meant by instinctive shooting, with the bat representing the bow.
Again... I'm in no real position to chime in here. And I'm happy with people shooting however they want—I taught my son to gap shoot because I was tired of lost arrows. But saying that there's no such thing as instinctive is like claiming a baseball coach can't warm up his team without the help of something more than years of swinging a bat and knowing how to make the ball go where he wants it to go.