I am also right-handed with a dominant left eye. Many years ago, someone came up with a method for people like us, and it was called the "Quell Method". By using a slightly modified Weaver stance/position, you drop your right cheek onto your right shoulder and aim with the left eye.
On the other hand, by getting in a lot of practise while aiming with your right eye, you can overcome the "dominance" of the left eye. You might want to wear an eye patch on the left eye for awhile, then eventually without the patch, but still aiming with your right eye.
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