No, I'm familiar with parallax as found in a magnifying instrument. I've rebuilt the odd scope you see.
What I'm attempting to say is that from what I was told, if your eye(s) is/are very slightly, and this is something so slight it cannot be seen in the mirror, cast or crossed, you will not get consistent results. ie: if you were to fix the rifle in a vice with sight mounted and repeatedly close your eyes & move your head and take a 'new' view 'through' the sight each time, the point of aim will not always be the same.
I should add that this is something I was told after I noticed this phenomenon myself and tried to find out why. It's 7 or more years ago, and I don't remember who I talked to, but it was probably Trijicon.
I suppose it could be caused by something to do with how the brain overlays the input from each optical nerve as well. I remember I was rather disappointed at the time as I like the OEG a lot and wanted to use it.
Yes, I'm aware that the dot is only visible within a certain plane - picked that up real quick I did.
As for the barrel mount, it's a one inch tube so if you're handy with a screwdriver, you could mount it on the base of your choice I guess. I was thinking of a scout type mounting.
Let me know if I can help further.