Hi,
I'm also Left eye dominant and right handed, and have had terrible trouble hitting my irons solidly off a tee, I know your pain!! And although a lot of advice is well meant, we are a "special" and need to tweak things a little to get the normal methods to work. No right handed, right eye doninant person would understand our problems fully, because when we look down the line, even if we know we're lined up correctly, it just looks wrong!..
Anyway, after many hours surfing and many hours practising and playing, these are my findings and this seems to work for me.
Grip - I use the Vardon grip, left thumb down the shaft, right hand "V" pointing between my chin and my ear.
Stance - I use the Leadbetter stance with my feet splayed out to 20° ( I do this because I also have the happy habbit of swaying in my back swing - Old Git problem!!) - stance parallel to hole. I also try to get my chin aimed at the logo on my club shafts
Ball position - I use Nicklaus/Hogan method, keeping my ball 2" inside of my left heel - for all irons and hybrids. And I put the ball name (or line) along the direction of the intended target, helps line me up.
Teeing up of ball - I usually use old discarded/broken tees (found lying around all over the course), and tee the ball up so that I can just, and only just get the tips of my fingers under the head of the tee.
I concentrate on hitting the inside quarter of the ball (eg - between 3 and 6 o'clock).
I turn my head slightly to the left (very slightly). And try to make sure I take a divot like an ordinary iron shot..
Hope this helps, as I've said, it works for me. Good luck.