I too am a righty who is left eye dominant. I was a horrible shot with the M-16 when in the USAF. It kicked the brass out into my face. By the end of qualification the right side of my face was a bloody, burned mess. My scores were terrible because I was flinching to try to avoid the brass.
I was in the Army, and qualified Expert. Was the hot brass coming at you a potential problem? Sure, but I was able to just tune it out, so that there no other factors but me, and my targets. Not everyone can do this, I know, but it can be done...
the infowarrior