The key to the issue is the preponderance of evidence standard. While it does not meet the " beyond a reasonable doubt" standard that isn't the historical standard used. Jefferson is not on trial ( though by the agonized writhings of the far right and far left on this issue you would swear that they have Jefferson in the dock.)Now, I don't have a dog in this hunt, as far as being a Jefferson-worshiper or hater, though I do tend to believe that (with rare exceptions) any one of the Founding Fathers had more character in his little finger, than all of his contemporary, pc detractors have in their entire bodies and souls. Then again, we're talking sex here.
You and I have some seriously incompatible standards, so we may have to simply agree to disagree. You speak of "probability" and of "the preponderance of evidence standard." Now, while I'm insufficiently corrupt to be an academic historian, I have conducted some historical research here and there (unsoiled by academic interference), and done some work on philosophy (of the social sciences, physical sciences, etc.), which I hope you won't hold against me.
History doesn't work based on probability or preponderance of evidence (civil court standard). It doesn't even work based on "beyond a reasonable doubt" (criminal court standard). You wouldn't happen to be a civil attorney, would you?
David Hume came up with a standard for the examination of claims of miracles, that I believe applies perfectly to radical, new social scientific and educational claims. I believe it works for all three so well, because the three types of claims have the same structure. In each case, someone makes an experiential claim that contradicts all commonly known experience based on the senses and scientific laws. The miracle claimiant would have us suspend all experience and scientific laws, and give him the benefit of the doubt. But as Hume argues, someone making miraculous claims must be held not to a lower standard of proof, but to a much higher one, if we are to trash all prior experience and science, on his behalf.
The Hemings Party demands that we throw overboard everything we know about Thomas Jefferson, and accept their miraculous claims. But those claims fall apart under scrutiny. Hence, we have no reason to accept them. And we certainly have no reason to accept the rules of inquiry the Hemings Party would foist upon us.
No...I'm not a civil attorney but perhaps their influence has become apparent over the years. I am a forensic accountant and work with civil attorneys in the preparation of suits arising out of fraud and malfeasance. Perhaps they have stained my thinking through the years.
In this issue I strive to stick to the issue of probablities versus cultural assumptions arising out of myth, politics, race or hero worship. Jefferson is one of my heroes based upon his intellect, vision, and decency. If there was ever a man with an inherent concept of noblesse oblige it was Jefferson. It is imcumbent upon me to divorce myself form my admiration of Jefferson. But as you say, Jefferson was also a man and subject to the same passions and digressions from some idealized path as other men of great and lesser character.
I do object to the phrase " The Hemming's Party" which tends to clearly telegraph the position long before the analysis. A kind of verbal variant of the Texas Sharpshooter effect. Much like those who assert that Jefferson is absolutely and incontrovertibly the father of Hemming's child, those who absolutely deny the probability, (or in some case even the possibility) that Jefferson is the father of Hemming's child use much the same process. Each draws his target around the requisite number of bullets to score the appropriate and specious bulls eye.
I've a colleague who has coined what he humorously calls " The Man Fron Planet Borgon Approach" In any issue that is larded with vested interest or close held belief he suggests you hand it off to a notional " Man From Borgon". The man from Borgon has no experience with the culture, history or values of the question at hand. You hand him the data as it is and let him count and then give a summation of the probabilities. He isn't black, white, liberal or conservative, He's a Borgonian. In fact he hasn't clue what the hell the issue is about merely that he has been asked to decide. He most assuredly "has no dog in this hunt". The Man from Planet Borgon doesn't even know what a dog is.
Now...It is my opinion that The Man from Planet Borgon would come to the reasonable conclusion that on the totality of the evidence it is more likely than not that Jefferson was the father of one or more of Hemming's children. While it is difficult to put some numerical expression to that likelyhood I would put it at about 70% I do not exclude the possibility that some other Jefferson relative was the father. I put that possibility as significantly less at 30%.
While that may seem subjective it is, to some degree, based upon some familiarity with the data. It has to do with number of total access days of each of the possibles. While Randolph is often bruited as the " real father" and it is possible, his total number of access days in the requisite period are extremely limited.
There you have it..
Jefferson is still my hero and all's right in the cosmos.