As far as I know, no one has ever constructed a stemma for Fulcher of Chartres. There isn’t one in Hagenmeyer, as you mentioned, or in Fink's translation. Fink is actually the editor of the English translation by Frances Rita Ryan, who translated Hagenmeyer’s Latin edition, but neither Ryan nor Fink discussed with the manuscript tradition.

It might be difficult to make a stemma. There are actually three different versions of Fulcher’s chronicle. The first version was written around 1105, and publicized in Western Europe, possibly as part of a call for a new crusade. The 1105 version was known and used by other historians, including Bartolf of Nangis, Guibert of Nogent, Ekkehard of Aura, and Ralph of Caen. There are no surviving manuscripts of the this version, but we can tell that Guibert et al. used it - for example, Guibert uses Fulcher’s description of the miracle of the “Holy Fire” that failed to appear in the Holy Sepulchre in Jerusalem at Easter in 1102. In the later versions, Fulcher rewrote this part of the text, so the story was shorter and more vague.

The second version was a sort of “new and improved” edition, where Fulcher expanded his original work up to 1124. This is kind of confusingly called the “first recension”, since it’s the earlier version in the surviving manuscripts. But then he also edited and expanded the text again, up to 1127, when he probably died. This is the third version, but Fulcher’s “second recension”. These latter two versions were used as a source by Orderic Vitalis, William of Malmesbury, and William of Tyre.

There are no manuscripts of the 1105 version, eight manuscripts of the “first recension” from 1124, and seven manuscripts of the “second recension” from 1127. The manuscript traditionally labelled as “A” is in the Bibliothèque nationale in Paris (ms. lat. 14378), and it’s the basis for the text in the Recueil des histories des croisades (RHC Occ, vol. 3). At the time, in the mid-19th century, the editors didn’t realize the difference between the two recensions, so they used this manuscript because it appeared to be the earliest one.

By Hagenmeyer’s time, the difference between the recensions was known, and he chose to use the second recension as the basis of his edition. His base text is manuscript 882 of the Douai municipal library. He kept the traditional names of the manuscripts, so the Douai manuscript is manuscript “C”.

Hagenmeyer also has a lengthy introduction that lists all the manuscripts and their characteristics (part 7 of the introduction, pg. 91-104). There is some codicological analysis there, but probably not as detailed as you’re looking for.

Since you're in Belgium you might be able to visit some of the manuscripts in person (well, maybe not right now, during the pandemic...) BNF ms. lat. 14378, the basis of the RHC edition, has been digitized: https://gallica.bnf.fr/ark:/12148/btv1b9067146g

The Douai manuscript has only been partially digitized, and I'm not sure if any of those folios are from Fulcher's text: https://bvmm.irht.cnrs.fr/consult/consult.php?reproductionId=11294

Sources:

Fulcheri Carnotensis Historia Hierosolymitana (1095–1127), ed. Heinrich Hagenmeyer (Heidelberg, 1913)

Fulcher of Chartres, A History of the Expedition to Jerusalem 1095–1127, trans. Frances S. Ryan, ed. Harold S. Fink (University of Tennessee Press, 1969)

Edward Peters, The First Crusade: The Chronicle of Fulcher of Chartres and Other Source Materials, 2d ed. (University of Pennsylvania Press, 1998)

Jay Rubinstein, “Guibert of Nogent, Albert of Aachen and Fulcher of Chartres: three crusade chronicles intersect”, in Writing the Early Crusades: Text, Transmission and Memory, ed. Marcus Bull and Damien Kempf (Boydell & Brewer, 2014)

Marcus Bull, “Fulcher of Chartres”, in Christian-Muslim Relations: A Bibliographical History, Volume 3 (1050-1200), ed. David Thomas and Alex Mallett (Brill, 2011)

There is one other source that seems like it would probably be useful, but unfortunately I have no access to it:

Verena Epp, Fulcher von Chartres: Studien zur Geschichtsschreibung des ersten Kreuzzuges (Droste, 1990).

Epp’s book is apparently the most thorough and up-to-date study, so hopefully you can find a copy.