Its an interesting situation to be in.
My brother and i were both in this position around 25 years ago - both right handers but left eye dominant.
He stayed shooting right handed, while i shot left handed. The end result was pretty similar, with both grabbibg national clay target titles.
We can both shoot of either shoulder, but i find shooting off my weaker shoulder becomes an issue after a couple of hundred targets.
My suggestion is to go with what works. Try both, but it sounds like what you are doing is working
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