From Fr. Chazal's upcoming book:
http://tradidi.com/resistance/contra-cekadam-part-1CARDINAL BILLOT sj... wrote the famed “de Ecclesia” and is at once the clearest, among many, to expose how your theory of sedeprivationism does not makes sense. Billot formulated the following thesis: “The peaceful and universal adhesion of the Church was always the infallible sign of the legitimacy of the person of the Roman Pontiff and the existence of all the conditions that are required for the legitimacy itself.” The proof is extensive (p.623). he states before that “From the moment in which the Pope [like Paul VI at least] is accepted by the Church and united to her as the head to the body, it is no longer permitted to raise doubts about a possible vice of election or a possible lack of any condition whatsoever necessary for legitimacy. For the aforementioned adhesion of the Church heals in the root all fault in the election and proves infallibly the existence of all the required conditions.” (de Ecclesia, I, p.612.) “…God cannot however permit that the whole Church accept as Pontiff who is not so truly and legitimately (this is precisely what you contend, from John XXIII to 1975 at least). […] this adhesion of the Church heals in the root all vice of the election and shows infallibly the existence of all the required conditions.”
If I mention his refutation of your sedeprivationism first, it is because Billot uses the universal adhesion of the Church to solve the mystery of the heretical Pope: “Whatever one thinks on the above sentences (Cajetan versus Bellarmine), the adhesion of the Universal Church shall be always of itself alone the infallible sign of the legitimacy of the person of the Pontiff, and the existence of all the conditions required of the legitimacy itself” (#3, p.634).
Moreover, on the question of loss of Faith in Rome, if Billot follows Bellarmine’s fifth opinion, (like Naz and the other manuals you quote,) he considers it a pure hypothesis that cannot happen because the tribulations of the Church would be unbearable: “Being verified the hypothesis that a Pontiff became notoriously heretic, the Church would fall into so many and such torments, that it is credible a priori that God would never permit this to be.” (p.632).
He goes as far as even deny the possibility of even internal heresy in the Pope, while most theologian, like the DTC, deny such impeccability in the Faith : “… if, considering God’s Providence, he Pontiff cannot fall into occult or purely internal heresy, much less can he fall into external and notorious heresy. The order established by God demands that, as a private person, the Sovereign Pontiff cannot be heretical, including in the sole internal forum.” (de Eccl). Hence despite his great clarity on other topics, Billot is confused on the question of the Heretical Pope. If you use him on this question, you have either to endorse his specific weakness on this question (belief in the Impeccability of the Pope), or to accept the solution he proposes to the conundrum: Universal and Peaceful Acceptance.