Great thread! As far as I’m aware the Venice arsenal marks would be either a C.X. for Consiglio dei Dieci or the Lion of St. Mark. So it seems to me that the twig mark must be an identifier of origin for the purchaser and seller alike. It might also have been something of a quality standard mark that it had passed tests by a guild. Marca a Mosca is probably a descriptive term (like “twig” mark). I think Fernando is onto something when pointing to Boccia & Coelho mentioning the mark as ferri di mulino (iron mill) marks. On German swords carrying the twig marks you might consider the possibility that these were North Italian blades with fake Solingen marks, rather than the other way around.
I wish I could find more to read on this in the English language (like Gotti’s Caino book!). You may find this of interest: https://www.hema-minsk2019.org/base...hibition-part-3
. It mentions a Beluni knot.