AI AXMC/AX MKIII in 338 Lapua Magnum and 308 Win for left handed shooter?

A little not going right handed, is that if I would have a failure of some kind,I could potentially get something straight into my right eye.
Yup, that is why I never use an RH rifle. Not to mention that you would break your rear bag position on each shot.

Being left-handed and an AI shooter, you have to be patient. I would wait for the AXSR but unless you buy parts now, you may find yourself in the same situation.

I am planning to buy an AXSR this summer. I already purchased all of the bolt bodies and a spare firing pin/shroud assembly. They just sit in my closet waiting.
 
You are lucky they make anything LH , most donot , see IF Sako make a LH TRG , yeah Naa , also if you using a rifle that is heavy in weight , its more often going to be supported by either a bipod or tripod , as such , why not run it from your Left side , But cycle the bolt with your right hand .The only use of a LH bolt is shooting un-supported in my view .
I am right handed and right eye dominate , but have thought of using a LH bolt , shooting from the LH side , left eye , and using my master hand to cycle bolt , the only down side is 2 fold , un-supported posn & weaker arm ( ie non master ) this is 2 fold the strenght in arm is less , as well as strenght in finger ( trigger ) , faster cycling and no breaking firing posn etc .
So you can over come some of the downsides by , using a sling & a lighter pull weight trigger .
You should try running a left handed gun right handed and see how you like it. As your only gun. Do you reload? Try shooting reloads and see how long you run it. Or would you prefer to have a right bolt gun?