I've explained this many times. Theologians classify papal legitimacy as a dogmatic fact. It must be known with the certainty of faith that a pope is legitimate because otherwise no dogmas defined by said pope could ever be known with the certainty of faith.
This example here sums up the problem with straight sedevacantism. Let's say I felt at the time of Vatican I that papal infallibility was heretical. All I'd have to do is to say that Pius IX was a heretic and a non-pope in order to reject the dogma. Consequently we must have a priori knowledge of papal legitimacy to preserve the entire Magisterium.
Since you've entirely ignored this argument, I'll quote myself.
In the example given above, please explain why it would have been wrong for that person to reject Pius IX as a heretic based on the belief that infallibility was heretical (some people did in fact believe that, by the way).
Was Vatican I the first time the Church taught papal infallibility? Was 1854 the first time the Church taught the Immaculate Conception? Did these teachings contradict prior Church teachings? I have never heard that they did.
Are there answers to these questions?
Both of those definitions are taught by the Ordinary Universal Magisterium. Very few bishops were against the defining of papal infallibility, in fact the majority of the those who opposed it's definition only opposed it at that particular time for political reasons. Cowardly and self-serving, but not actually heretical. Very few actually opposed it on a "doctrinal level" and those who did are who we've come to know as the "Old Catholics."
Ladislaus poses a point that has some truth to it, but I don't think it's a difficulty for the sede vacante position. We accept the faith on the authority of God, and the Church he founded. So, morally speaking, it is necessary to know the identity of those who comprise the hierarchy, and at this time we (or at least, myself and everyone I know!) is unaware of who and where they are. God provides, of course-- it's no accident that this crisis comes at a time when certainly legitimate authorities (although dead) are available so easily.
St. Paul says that if he, or even an angel from Heaven teaches a foreign gospel, let him be anathema. We reject the Novus Ordo program because it is contrary to what we have already received and believed on the authority of the Church. And we also know that such an instance (being proposed a false faith by one who appears to be an authority) is possible based on this.
Anyways, back to the immediate point, both of those doctrines are taught by the OUM so one who would deny the legitimacy of Pius IX on the grounds Ladislaus describes is not following St. Paul's instruction where traditionalists are.