After some research, im not so sure about your sources. in D'Elia's book that came out it specifically says Bufalino took over after Sciandra. It also says Barbara was dispatched to binghamton to oversee Magaddino's operations. As for Carmine Lombardozzi, he contradicted himself. Heres an exerpt from Ed Valin's great article (https://mafiahistory.us/rattrap/inflatorre.html#n37)

"Lombardozzi told agents he first met Bufalino in 1957 at the mob meeting in Apalachin, New York. He had attended Apalachin as part of the Gambino Crime Family delegation led by Carlo Gambino and Paul Castellano. According to Lombardozzi, "Bufalino was introduced [to him] as the head of the family in Pittston, Pennsylvania." [45] He said Bufalino's crime family had fifty members scattered throughout the surrounding towns. He said Bufalino wasn't a Lucchese Crime Family member. At the time Lombardozzi first met Bufalino, Joseph Barbara was still alive. (He died of natural causes in 1959.) If Bufalino were the boss then, that would mean either Barbara was subordinate to Bufalino or Barbara was a member of another crime family altogether. In another debriefing, however, Lombardozzi advised, "Joe Barbara, when living, was the head of his own 'Family' and was the boss. The 'Family' which Barbara headed is now known as the 'Bufalino Family.'" [47] The contradiction between Lombardozzi's two statements is left unexplained in the available FBI reports."

LaTorre's brother Sam also never mentioned Barbara being boss

Joseph did say Barbara was the boss and this is good info to have. Overall though, i dont think we really have enough evidence to make a definitive ruling.