Zeroing Red Dot Sight?

Now a break from my usual musings and rants to throw a question out there and see if anyone has any ideas about what is going on.

I recently received a Burris Fast Fire 3 red dot sight.  Put it on my AR and went to zero it.

Pertinent information:  I am cross-dominant.  That, of course, means that I am right handed but my left eye is dominant. In shooting handguns this is really a minor consideration, since the handgun is not mounted to a shoulder – all one needs to do is shift the position of the handgun to the line of sight of the (cross) dominant eye.  In shooting long guns, as in during my 10 years in the Army, I always fired right handed but closed my dominant eye so I could sight with my non-dominant eye.  I always qualified as an expert marksman.

With that as background, I mounted the red dot on my AR and went to zero it.  I used my standard approach – close dominant left eye, aim with non-dominant right eye.  Initial points of impact were about a foot low and a few inches left –a good group, but off target. Adjusted windage – shots were now about a foot low, directly below the aiming point – good group but a foot low.  Adjusted the elevation, no change, adjusted the elevation, no change, took elevation change to its limit, no change.  I never could zero point of impact and point of aim. Backed off of the limit and still not change. 

So, I decided to shift over the shooting left handed and using my dominant eye.  Good group, 4 inches high (!?!?!).  Adjusted elevation to bring point of impact down and there it was – shooting left handed, using dominant left eye, rifle zeroed…Shot right handed using non-dominant eye – off target. Shot right handed, both eyes open, blurry double image, but one dot on target – bull’s eye.

Another bit of pertinent information: Although I have presbyopia, I have never had any real vision problems with either eye – no pre-existing right eye issues have my vision tested every year and had the last exam about 2 months ago. Have zeroed by scope on this same AR using my usual right handed/non-dominant eye approach before with no issues.

Anyone have any ideas on what is happening here?  Why would I be unable to get the red dot to zero using my usual, if unorthodox and not highly recommended approach, but then can do so if I fire left-handed and use my dominant left eye?  Shouldn't either eye be able to basically adjust the point of aim (the dot) to match the point of impact?

Would love to read any speculation.