Actually, the idea that it comes from "Gastaldo" is rather interesting, as the northern part of italy borders on france. Linguistically, Gastaldo is very similar to Castaldo, which more literally is Italian for a person who raises a drawbridge. A castaldo raises a drawbridge. The derivation castaldi seems to be derived from the Italian language, as the masculine singular "castaldo" would be changed into the masculine plural "castaldi", or a group who were "stewards" AKA, guarded the gate, raised the drawbridge.
Logically, it follows that a family who was well regarded in their trade may take the name of the trade. For example, the english "Smith" derived from (Black)smith, "butcher", "farmer", etc...
This seems to fit with the family coat of arms, awarded by the deMedici family. Correct me if my history is wrong, but I believe that Venice is the home city of the deMedici family.Further, there is some reference to a general Castaldo fighting an austro-hungarian border war (N.E. Italy) in around 400 AD. I don't know if this is where the family coat of arms comes from, but it certainly is plausible that if General Castaldo did a good job defending the deMedici lands, then he might have gotten a coat of arms for his good service and stewardship to their realm. (I realize this is a stretch, but it seems to fit).
As far as the "Gastaldo/Gastaldi" derivation, being so close to the Gaul(French) and Germanic territories, I can imagine Castaldo becoming its linguistic equivalent in those regions. Correct me if I'm wrong, but there's no hard "C" sound in French. Hence "Gastaldo" from "Castaldo". As Italian has a hard "G" sound, it doesn't seem to follow that it would go the other way.
I'm curious about the connections between Rome, Naples and Sicily that you've discovered. I'm assuming that there are Castaldo families in those regions? What have you learned?