I'm curious what the left-eye right handers and right-eye left handers do in terms of shooting?

Personally I'm left eye dominant but my right arm is my strong arm, I write left handed but I do everything else right handed by instinct (baseball swing, ping pong, pistol/rifle, etc.). When I was a kid I used to shoot right handed and couldn't hit the broad side of a barn because my left eye was focusing in on the sights, these days I mostly force myself to shoot left handed, but I've been considering practicing more my right hand because it feels more natural, I just have to cock my head/pull my arm inward or some combination of the two.

How have you other cross-dominant shooters responded to this conundrum? My initial instinct was to stick with what my dominant eye tells me to do, but these days I'm thinking maybe I should just make lemons into lemonade and work seriously on my ambidextrous shooting.