Well, commonalities are what we're looking for. Are there constants?
Just to take transition as an example, are the 8th house and the Ascendant (death of the body) constants? Are Saturn and Pluto constants? Are Jupiter and Neptune (liberation and expansion of consciousness) constants?
Yes there can be endless permutations of factors involved. What signs, what aspects (harmonious or hard), and yes, the timing.
Of the three cases I've touched on here (Jayne Mansfield, Sharon Tate and Marie Antoinette -- granted, hardly a definitive sample) are there constants? Does one technique of depicting operative celestial influences work better than others?
I'm not maintaining these are anything but open questions.
What if the matrix IS the mission?
Would a soul pick a matrix incompatible with their mission?
What does "matrix" mean to you in this context?
I get the wisdom in your starting with a few women to focus on, in-depth. However,....
To put (what I see as) your project in perspective, we should move on to a big sample of research subjects. We might give each natal chart a couple thousand data points, some weighted more than others. These are the independent variables. Then we would be looking at even more data points with various prognosticative methods. To put it statistically, this is one big data set. Then I think you'd need some kind of multivariate statistical method to analyze all of this. You'd be looking for correlations that are significant beyond random chance (which the computer works out for you.)
Which is probably why the small statistical tests conducted so far haven't been wildly successful. The Gauquelins deserve a lot of credit for their innovative work; but it is fraught with methodological problems, as well (like rounded birth times.) Sadly, I don't think most astrologers have the background to do this kind of research; and then most statisticians and computer programmers don't have the astrological background.
David Cochrane has done some interesting work with large data sets, but I find his methods to be really problematical.
On the Rodden "A" rating, I think it's probably fine. Royal births like Louis XVI would have been closely timed. In France, civil birth records had to await Napoleon Bonaparte's reforms. And then, they were generally timed to the nearest hour, not to the minute. I found this out once, in looking for commonalities in the birth charts of French-born painters. I checked out Austria, where they didn't begin until 1939 under the Nazi regime.
However, because Marie Antoinette was such a public figure, it should be possible to put her chart through some basic rectification methods, and see if the timing is accurate.
Part of the reason why I don't think your project will be such an easy process is that the births of one's children are standard rectification data points.
I had two children with natural childbirth methods, so no invasive medical intervention. Also, in Placidus, I have Mercury, Venus, and sun in my 5th house of children. Both babies were wanted and loved. Their birth moments have different signatures in my chart.
Within 1 degree of orb, My daughter's sun conjuncts my ascendant. Her Venus opposes my sun. Her Jupiter-Uranus sextile my Mercury-Venus. Her Neptune conjuncts my IC. Sticking to a 1-degree orb, I'm not seeing anything similar when my sun was born his NN (true) conjuncts my ascendant. His Pluto conjuncts my Neptune, but that would encompass a lot of people. My sun's solar arc moon conjuncts my Saturn at a bit over one degree. His Jupiter is in my 5th house, but no direct hits. Not much with secondary progressions. My progressed moon hits his Saturn.
There may be something somewhere to my 5th house, but it's not obvious with the most basic of prognostication methods.
I could go on like this, but obviously, part of the issue might be the ever-changing sky. (Not stepping in the same river twice.) My children are very different people, not only because of different genders. My experiences of raising them were very different.
I think the answers lie elsewhere. Like in the mind of the astrologer.