Leaving aside the fact that Sean is being obnoxious, though, I don't see why "they're legitimate popes, but we've exaggerated the universal ordinary magisterium" is *off the table* as a solution.
Keep in mind that Papal Infallibility itself was debatable up till 1870. Vatican I dogmatically affirmed it under limited circuмstances. Maybe trying to go beyond that, or trying to say the ordinary teaching authority" of the Church in one particular era is certainly infallible, is a problem.
In my own mind, this has crossed a line. Clearly not everything ever taught by any Pope ever is infallible. Unfortunately, many sedevacantists exaggerate the scope of infallibility ... as an overreaction against R&R. But I think we've crossed a line from the mere technicalities of infallibility into what I would consider to be a defection of the Magisterium and Universal Discipline. I subscribe to Monsignor Fenton's line of thought on this matter.
It might be definitely understood, however, that the Catholic’s duty to accept the teachings conveyed in the encyclicals even when the Holy Father does not propose such teachings as a part of his infallible magisterium is not based merely upon the dicta of the theologians. The authority which imposes this obligation is that of the Roman Pontiff himself. To the Holy Father’s responsibility of caring for the sheep of Christ’s fold, there corresponds, on the part of the Church’s membership, the basic obligation of following his directions, in doctrinal as well as disciplinary matters. In this field, God has given the Holy Father a kind of infallibility distinct from the charism of doctrinal infallibility in the strict sense. He has so constructed and ordered the Church that those who follow the directives given to the entire kingdom of God on earth will never be brought into the position of ruining themselves spiritually through this obedience. Our Lord dwells within His Church in such a way that those who obey disciplinary and doctrinal directives of this society can never find themselves displeasing God through their adherence to the teachings and the commands given to the universal Church militant. Hence there can be no valid reason to discountenance even the non-infallible teaching authority of Christ’s vicar on earth.
...
It is, of course, possible that the Church might come to modify its stand on some detail of teaching presented as non-infallible matter in a papal encyclical. The nature of the auctoritas providentiae doctrinalis within the Church is such, however, that this fallibility extends to questions of relatively minute detail or of particular application. The body of doctrine on the rights and duties of labor, on the Church and State, or on any other subject treated extensively in a series of papal letters directed to and normative for the entire Church militant could not be radically or completely erroneous. The infallible security Christ wills that His disciples should enjoy within His Church is utterly incompatible with such a possibility.
This is my understanding of the Holy Catholic Church as well. With Vatican II and the New Mass, we are not talking about an isolated passing thought in some Encyclical. What we have here is a new theological system. Along with it has come a Mass that has done grave violence to the Church's revered Liturgical Tradition. My faith in the holiness and the indefectibility of the Church rule out this possibility as a matter of faith. I believe this with the certainty of faith.
See, a material continuity of the Church does not suffice for indefectibility. If the Church can by her official teaching and discipline bring grave harm to souls, where we feel that we cannot in good conscience participate in whatever this is, then the Church would have defected in her mission. At that point, what good would a mere material continuity be? In that case, souls would be better off if such an institution were in fact to go extinct. It's one of the main reasons Our Lord left the Church with teaching authority, so that the sheep in heeding it would be kept from going astray, and not in order to lead them astray.
If I were to tell St. Robert Bellarmine that I considered it a possibility that the Church could hold an Ecuмenical Council that endangered the faith and a Roman Rite Mass that harmed souls, he would unquestionably without the slightest hesitation declare me a heretic and outside the Church.