Now it may be, when the Church one day comes back to her senses, that the alone competent authority will declare that the Conciliar Popes were not Popes, but between now and then the arguments so far brought forward to prove the See of Rome to be vacant are not as conclusive as they can be made to appear.
His Excellency Bishop Williamson is not a sedeplenist; he is a sede-doubtist, just like myself.
Sede-doubtist is a new term for me, but how it is possible that anyone can know with absolute certainty that any pope is pope, much less the VII popes?
Ah, you ask the right question. Pre-Vatican II theologians dealing with the question of papal legitimacy classified it as a dogmatic fact, fact because it's in the nature of an event rather than a doctrine, and dogmatic because it's so intimately tied to dogma that it must be believed with the certainty of faith. So, for instance, if I'm living during the reign of Pius XII and he's defining the Dogma of the Assumption, I cannot have the certainty of faith regarding the Assumption if I do not also have the certainty of faith regarding the legitimacy of Pius XII. That follows according to the logical principle: peiorem partem semper sequitur conclusio
So then, for instance, a prominent theologian writing during the reign of Pius XII said it would be heresy to reject the legitimacy of Pius XII.
Then, to get to your core question, theologians usually cite Legitimate Election + Universal Acceptance as the a priori
criteria for establishing the legitimacy of a pope with the certainty of faith. NO CATHOLIC ever doubted the legitimacy of Pius XII, so we know that he was legitimate with the certainty of faith due to the indefectibility of the Church.
Of course, it all gets a little more mirky and nuanced with the V2 Popes, and I'd rather not get into the theology of it here as it's been hotly debated in the Crisis section of CI. But I'll segway here into your next point.
I seem to recall Archbishop Lefebvre himself admitting to doubt in this matter.
Correct. And here so does Bishop Williamson. Bishop Tissier has made even stronger comments. If +Lefebvre and +Williamson and +Tissier say that it's POSSIBLE that we'll know some day that these popes have been illegitimate or that it's POSSIBLE for a good Catholic to hold (at least as a private opinion or well-formed doubt) that these popes MIGHT be illegitimate, that by itself PRECLUDES their holding V2 Papal Legitimacy with the requisite "certainty of faith", for, you see, certainty of faith absolutely precludes any possibility of the opposite being true.
So at that point one enters into what theologians classified as a "Papa Dubius" ("Doubtful Pope") position. So these theologians formulated the maxim, "Papa Dubius Nullus Papa" ("a doubtful pope is no pope"), meaning that these popes effectively lose authority as a result because, SINCE THERE'S DOUBT, they can no longer be upheld with the certainty of faith as a rule of faith. Father Jenkins cited a theologian who writes that such popes no longer FORMALLY exercise authority even if materially in possession of the See. Canon Lawyers also state that one is not guilty of schism if refusal of submission to the Holy See stems from widespread, grave, well-founded positive doubts about their legitimacy.
Father Chazal recently used similar language, that they have lost authority and can be "disregarded" due to their public heresy; he referred to them as being in "quarantine".
That's the position I have adopted, what I call SEDE-DOUBTISM. Yes, it's not surprising that the term is new to you; that's because I made it up (partly tongue-in-cheek but to make a strong point). And I hold that neither +Lefebvre, nor +Williamson, nor +Tissier are SEDEPLENISTS in the true sense because they do not hold to the legitimacy of the V2 papal claimants with the certainty of faith. This justifies what Father Chazal referred to as a categorical "disregard" for their "authority". It's akin to the theory called sedimpeditism except with a greater emphasis on the principle that Church authority would be required in order to definitively answer the question and eliminate the doubt. I reject SVism because it allows individual Catholics with their private judgment to EFFECTIVELY depose popes and disregard their authority. We can do no more than to raise the doubt but defer to Holy Mother Church to definitively answer this question.