I'm also left eye dom/right handed.Never had a problem with right handed guns.Even when I was in the army I shot that way.Tried changing,but couldn't train the right eye to take over.Finally had sergent told me to which back.SaidI shot better that way than most right hander's ever though of shooting.Shot 38 out of 40 on my final test.All my guns are right handers except my winchester model 94.Its pre 64 and it top ejects so it just throws the empties over my head.