Maybe it would help if we would know the meaning of brito. Do you know whether it exists as a personal name or noun in Ladino/Judezmo? I can't find it in modern Spanish dictionaries.
I've speculated that the version Britos may have been formed on other Sephardic names in my father's village, such as Marcos and Santos. My father's village, Colmenar de Montemayor, is close to the province of Extremadura which has the endearing habit also extant in Andalusia and a large part of the Americas to "eat" the final -s- Meaning that it may have been a hypercorrection.
I recall receiving a letter by an almost illiterate relative of mine who had included a lot of final -s- which should not have been there :-) Something like: "Te escribo estas cartas, etc."
However, this would not explain the occurence of Britos in Castillian and Northern regions with a much more "s-friendly" mentality.