Being left handed and left eye dominant, but shooting right handed with both eyes open, I think I have a good answer for this.
One, have the discipline to LOOK AT THE TARGET. My pre-shot focal point is at a distance. When I see the flash of the bird, I am not likely to bring focus all the way back to the gun, after locking on the target. I simply know better, and so do you.
Two, a high shooting gun helps to look over the gun instead at the gun. My Sporter/Skeet guns shoot around 80% high, The Trap gun shoots about 100% high. With focus on the target, if I have to cover the bird with the muzzle, one eye usually still sees the bird.
Works for me, YMMV.
These days, my left eye is so much stronger than my right eye, if I close or block it, I am impaired on the line. No, although I CAN shoot left handed, after 53 years, I am not going to change over to please anyone. I have finally got the gun fit I want.
The three Brownings I now shoot are right handed guns, in operation as well as fit. I am very happy with them, and after shooting and owning most brands, including the "K" and "P" guns, they are my brand of choice.
These days, having outlived my family and two wives, I only have to please myself. LOL