I'm going to go out on a limb here with this. Please note that this is not fact, just theory. Work around the edges of this and the truth should come out.
You mention that you are better right handed only vs. two hand...and you mention that you are better left hand (off hand) than right hand (dominant hand). I am going to venture a guess that this has something to do with muscle memory. It also has to deal a lot with right/left brain hemisphere dominance. Right & Left brains being relative opposites (right side, creative - left side analytical...or something like that...) it makes sense that if you have NOT trained effectively with dual hand holds, the two brain halves are competing against each other instead of working in uniformity.
By the same token, your right hand 'should' have more strength than your left hand if your right hand is dominant. The result is that when two-handing a pistol the brain is trying to exert equal force on two hands...but the left hand doesn't have the staying power of the right and therefore they aren't working in sync with each other.
When using just the right hand there is no brain counteraction against the left because the left isn't involved in the picture. All your brain activity is focused.
I read a book once on Billiards (shooting pool) wherein the book says to chalk your cue with the off hand - the reasoning behind this is psychological. By forcing the other half of the brain (say, left side) to do the work, you effectively also clear the opposite side (right side) at the same time. This creates a moment of clarity which allows the pool shooters to focus both brain sides more effectively. It seems to me that this same concept applies here.
Now, here is where I can't quite back anything up - it's just theory. Your left hand doesn't have the muscle memory built up that your right does. All muscles are working at equal force (sorta) and are focused with all of your brain power. The lack of muscle memory and strength (ie: your right hand will have much stronger index and thumb muscles from all the writing you have done in your life...) means that you are NOT exerting improper force with the wrong digits on the firearm from overbuilt "normal use" muscles that your right hand uses.
I would be willing to bet that if you practiced a LOT with your left hand, you would find a three-stage build up. First, you would improve your left hand concentration and shooting. Second, you would eventually plateau your skills as your brain focus and left hand strengthen. And Finally, you would begin to lose a bit of your accuracy as you begin to doubt what the heck is going on and your brain goes "WTF???". A Fourth stage would occur, in theory, when you surrender and just accept your ability to shoot left handed, and your groups would tighten up again.
I do know that when it comes to benchrest shooting a rifle, my left hand (off hand) groups are actually better for about the first 10 shots than my right hand...after which my left trigger finger gets tired and I start to lose accuracy.
Just a theory, but I think the basics are there for any medical doctor to explain in greater detail.
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