I'll chime in here too, as I'm similarly skewed. I'm right handed, but left eye dominant, and I didn't even know it for years - I now shoot left handed. When I was a kid, I shot right handed. So, it came in handy that I took several years off shooting bow because when I came back into it last year, I started shooting with my left, and it was easy because I didn't have any muscle memory to overcome. At the beginning, though, (before I built up all my lefty muscles) there was a clear difference for me when I tried switching between left and right. Eye dominance was a factor for me, for sure.
The excercise that I enjoy most (where eye dominance plays a factor in depth perception) is shooting three different targets at different ranges, usually something like 8-12-15 yards, one after the other. It exercises your eyeballs instead of just your shooting muscles - sort of like how when you watch baseball players warming up on the field, the shortstop and third baseman don't just throw the ball back and forth to each other (which would be fine if they just wanted arm exercise), they're throwing to and catching from all different positions.
