At last I've got the paper I've promised you. You can download it there (739 k) but it's rather disappointing if you are not a trained egyptologist. The point is that the pharaoh whose name can be read at line 27th, is not "Caesar" but "Djeser" (3th dynasty king revered as a god by the Ptolemies like his vizir Imhotep) according to Devauchelle.
Line 27 : "writen in year 5, month 2 of akhet (inundation), day 25, Festival of Isis or birthdate of the pharaoh (life, prosperity and health) Djeser (life, prosperity and health)..."
Djeser, not Caesar. Consequently, the assumption is that the date, whatever it is, has nothing to do with Caesarion, neither with Caesar himself. So, when Carcopino juggles with julian and egyptian calendars to demonstrate that this date is in fact Julius Caesar's birthdate, because he was worshiped as a king all over Egypt, I find it highly speculative.
I'd like to know if this stela is the sole evidence of Cesarion's birthdate, because if so, and if Devauchellle is right when he reads "Djeser" rather than "Caesar", a birthdate in april -44 becomes interestingly plausible and if it is the case, Caesar is not his father !
Since I am dealing with Caesar's sons, I have put an interesting paper on my website, for those who can read french (Daniele Porte "la perle de Servilia " - note sur la naissance de Marcus Iunius Brutus, Revues des Etudes Anciennes 96, Bordeaux, 1994, pp. 465-484) (945 k).