I have seen long guns (mainly double shotguns/rifles and drillings) made in England or Europe with offset stocks, to allow a right side hold with a left dominant eye. But unless you want to take out a second on your house, and sell your youngest daughter into lifelone servitude, that probably isn't an option for you. So I would suggest basically what the others have, either shoot with the "weak side," (as a former longtime law enforcement weapons instructor, I have always hated that term), or learn to ignore the dominant eye and shoot with the other...
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OBG