Welcome to my new world!
I'm wildly right eye/side dominant...unfortunately, I've lost most of the vision in my right eye thanks to some botched surgery a couple of years back (that didn't quite make the legal definition of "malpractice").
After a certain period of anger, typical male stubbornness, by god I can do this, sort of denial, I sucked it up and started shooting right hand/left eye. I've always shot both eyes open as a competition shooter, and I initially thought my eyes would adjust to the left-eye-dominant on their owns. Didn't work...I had to go through a long period of closing my right eye to force my left eye to do the heavy lifting. I'm working on both eyes open again...I do notice a similar slightly to the left point-of-impact than shooting right-eyed and I'm still not as fast as I was in acquiring the sights.
Mounting long guns left-handed, now that't still a...challenge...LOL!
Michael B