In the course of that research I took a closer look at the Chronicle (about 235 AD) of Hippolytus of Rome and formed the mistaken impression that Hippolytus had been a believer in a certain inflated and baroque chronology which had been abstracted from the biblical Book of Judges by an early Christian or Jewish chronographer.
Finding one's way among the subtle differences in Antique chronography (which is only preserved in fragmentary manuscripts based on repeated revisions of the original works) is an immensely tedious and complex affair which has never been the main focus of my research. The modern scholarly analysis of this material often employs elaborate arguments which magnify the faintest of evidence to arrive at some kind of usable conclusion.
In this case, much of the argument turns on how many phases make up the Book of Judges chronology and which phases were included. My Studia Patristica article, which is already in press, states:
Distinctively Hippolytan elements in the account can be found for example in the period from Joshua to Eli inclusive, which is divided by the Great Stemma into 22 political phases. Hippolytan features here include the rule of an apocryphal judge Shamgar (6th phase) and his alter ego Samera (21st). Both phases were witnessed as present in the Great Stemma when it was seen by the author of the Liber Genealogus in 427, whereas their existence had been firmly ruled out by Eusebius. This would suggest that the author was either hostile to or ignorant of Eusebius.
However I have now read and re-read Rudolf Helm's 1955 edition of the Hippolytus Chronicle (particularly pages 164-167) and understood that (at least in the editor Helm's view), Hippolytus divided the period (Joshua to Eli inclusive) into only 20 phases and excluded the rule of an apocryphal judge Shamgar (6th phase) and his alter ego Samera (21st). These are tiny distinctions, but are enough to derail the argument that Hippolytus was involved.
Farewell Hippolytus: you are no longer on the Great Stemma team.
I have duly changed the page on my website that deals with the matter. In the Studia Patristica article, which can no longer be altered, I would now want to say that there are elements in the diagram which clash with the theories of Eusebius and plainly come from an older, as-yet unidentified chronographer. The misidentification of that chronographer as Hippolytus is a very minor issue, and does not in any way weaken the main thrust of the article: that the Liber Genealogus is a description of an early version of the Great Stemma diagram.
The necessary conclusion after dumping Hippolytus is that some other chronological tradition influenced the Great Stemma. Perhaps the chronographer involved was Julius Africanus, perhaps not. I am not intending to research the issue further. If my error proves to be the stalking horse for a future scholarly article by a specialist, so much the better. I would welcome scholars in the history-of-chronography field taking up the matter and giving it a thorough review.