By the way, as usual, I missed the part where it's explained how exactly sedeprivationism solves the epistemological problem.
It doesn't. That's why I have a different position in terms of the role of individual judgment that is not primarily focused on the legitimacy of a given pope, but, rather, on identifying the True Church of Christ.
John of St. Thomas articulated the
quoad se vs.
quoad nos distinction, arguing that the
quoad se is effectively subordinate to the
quoad nos, which I have come to realize is a seriously defective position. It's almost like a theological phenomenology.
As Vatican I taught about the process of supernatural faith, human beings use natural reason to identify the True Church founded by Christ from the rational motives of credibility, and then this Church determines who holds authority in it.
Traditional Catholics have come to the conclusion that the Conciliar Church lacks the Marks of the True Church of Christ and lacks those motives of credibility, that aspect of the process of faith that is rooted in natural reason.
Imagine for a second that Vatican II had never happened, and that there had never been a New Mass. Within this Church, then, we had a Jorge Bergoglio come to office. He doesn't teach error or heresy, but he's spouting heresies in his interviews with Scalfari or on his papal plane trips. In that kind of scenario, it's not our concern, nor is it our problem, and not our duty to address. We let the Cardinals handle it.
Another scenario that sheds light upon the matter is this. Let's look at one Cardinal Richard Cushing. That guy was as manifest a heretic as they get. "No salvation outside the Church? Nonsense." ... and that's just the tip of the iceberg. Did he remain the Cardinal/Archbishop of Boston? According to straight SVism, he did not. Yet most of the dogmatic SVs hold that he rightly disciplined Father Feeney. But by SV criteria, the man was not the Archbishop of Boston. Or was he? He was never removed from office by the Pope. Priests continued to receive jurisdiction from him for the Sacraments. And so forth. SVs need to answer what the status of a pre-Vatican II manifest heretic bishop who was not deposed by Rome (there were many such) ... and that status is analogous to the status of the post-V2 papal claimants.