I am cross dominate as well (the same as you left eye dominance/right handed) and I shoot left handed with my left eye. It feels more natural once you handle your gun more.
I also suggest practice with your right hand/eye by closing your left eye when shooting. It is useful to learn to shoot both left and right because you can switch and not overexpose yourself around a corner in a CQB environment.
Last edited by Fenrir92; December 16th, 2014 at 13:48..