Cross-eye dominant here; left eye, right handed.

Closing the left eye when aiming has worked well up until the last couple years, whereupon vision changes have reduced efficacy.

With small adjustments to stance, shooting now with both eyes open and lining sights up with the left eye is working nicely.

Bottom line: see what you need to in order to make clean shots.

As it stands, sounds like you've transitioned to red dots and are doing well with them; I'd leave it just like that.

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Pickpocket