My father used to be my spotter from across the table. I would set up a straight shot and he would say "The back of the cue is too far from your body. It isn't lined up straight." I would pull the cue toward me until he said it was perfect. I'd stand up and say, "You've got to be kidding. You need your eyes checked, you're nuts." Eventually I realized that smart phones with cameras were a godsend for this kind of thing and my approach was to do whatever I had to in order to have a straight initial set up, straight take back and straight follow through. I used the Mark Wilson adage of "Just because it feels right doesn't mean it is," and the corollary, "It might feel wrong and uncomfortable, but eventually you'll get used to it."
I've gotten things pretty well straightened out now, but I'm still tweaking things. These improvements do show up during actual play.
Also, why does not having a dominant eye prevent you from experimenting? Some particular position feels right to you. If you moved your head over 1/4 inch it would feel wrong but eventually I think it would feel right. Of course there is no reason to do this if you have a straight stroke.