Here's what I did.
I took a Ruger 22/45 with a long heavy barrel and target sights and I went to the local indoor pistol range that's open in the evening after work. I went through a few bricks, consciously shooting with my right eye instead of my left (my dominant eye and the one I had been using just instinctively).
I KEPT BOTH EYES OPEN. I made sure to do so. I just forced myself to use my non-dominant eye, but without closing my eye or using something like tape or an eyepatch. After about 2000 rounds, it was no problem. I still consciously do it with a pistol, just to keep it up.
Now I can shoot with either eye if I want, and I can shoot both-eyes-open with shotguns, rifles and pistols, and hit the bull without any issues from the two eyes. This is what you want to be able to do for shooting clays and for hunting, if you can. Peripheral vision, 3D vision and depth perception are all wonderful tools, not things to be indiscriminately thrown out in favor of a shortsighted "solution" to eye issues.
What never did work for me: tape on my glasses. Man, in the time it takes to get used to that, I can learn to shoot without it and have better vision. I tried it, and I really don't get it. My guess is, it's what instructors tell their students to do because they don't want to take the time to do anything better. It might be good for an improvement, but I really can't see how you won't hit a plateau that isn't an issue for people who don't need tape.
And what should I do when I'm hunting? Wear tape on my glasses? Not around here. I'm not fond of falling off boulders from screwed-up vision.
Am I a great shotgun shooter? No. You won't see my picture in magazines. Or anywhere else.
But can I shoot as well as anyone I know with the same level of experience, practice, etc., but without a history of cross-dominance issues? AFAIK I can. I
can say with confidence that, when I miss a target or bird, it's not because of cross-dominance.
Now YMMV. Maybe you can't learn to use your other eye.
But I, personally, think it's worth a try, vs. spending a bunch of time and effort on other inferior "solutions" first.