First I need to apologize for being slow in answering, and also for not being able at the moment to take the time needed to give a careful and well thought out review of your work. We are all busy of course, and my hope that retirement would make me a man of leisure has long been dashed, but this particular period has been (and will continue to be) pretty intense. More about that later at some other time.
Given my time constraints, and the rustiness of my pop gen skills (its been a while since I’ve used them) I have not checked your work in detail, but it seems to me to be generally accurate, or at least to make sense. As you indicated somewhere, (I cant find it at the moment) the population size of a bottleneck is inversely proportional to the length of time between the bottleneck and the present, given a particular degree of genetic diversity in the present. Thus, your result that a possible bottleneck of 2 about 500Kya seems plausible. And of course, we know that despite Dennis’ comment about modern human genetic diversity, humans are far less diverse than other, older primates, based on Wright’s Fst statistic, which is something like 2, as compared to about 10 for gorillas, if I recall correctly. So, based on this alternative approach, it seems that your result is certainly feasible.
Of course, what that explains is the potential for a bottleneck of 2 to allow for modern genetic diversity, which we all agree could not be possible if the bottleneck happened after 100Kya. The figure of 10,000 (I think 2000 to 10,000 is still used by some) cited by Dennis is likely the result of a bottleneck believed to have occurred as a result of the general die off following the Toba explosion around 70Kya that produced a global cooling and drying trend. But this says nothing about the possibility of earlier bottlenecks. So if the quest for a bottleneck of 2 is the goal, I believe you have found it.
The real problem for me, though is the theological implications. At 500Kya, no couple could have been anything like Adam and Eve, of course. They would not have been H. Sapiens, its likely they didn’t speak, probably couldn’t have worshipped God, their immediate descendants certainly could not have tilled the land or built cities, etc. The extent of their humanness, their possession of anything resembling Imago Dei, must be considered very limited.
And the issue also remains that theologically we cannot speak of bottlenecks so much as special creation. That is still possible with a putative common and restricted ancestry of 2 individuals, but quite frankly I don’t see the point. Even if your calculations are correct (and I believe they are), what you have shown is that all current human beings are descended from one and only one particular couple that lived before modern H Sapiens were a thing. And even if that couple were the result of a special creation, their immediate descendants still had to mate with the surrounding population. And then allow a further 200-300K years to pass for the evolution of H Sapiens to occur.
I find the genealogical argument that we are all descended from many couples who lived 6 to 10,000 ya, one of whom were Adam and Eve, people either created by God or endowed with spiritual gifts, to be far more compelling. I realize that some will reject the many couple idea, but they cannot use a literal reading of scripture to do so. The single creation event is interpretation, and as you know, I reject it.
So in summary, while I believe that your attempt to find a single universal MRCA of 2 people has probably succeeded, I find less value in that though, than I do in your earlier discovery of the genealogical common ancestry of all people in an historical Adam and Eve within a Biblical time frame.