Church councils are infallible only insofar as the pope makes them infallible. Whatever V2 was, there was no infallibility to it.
Both you Old Catholic R&R types AND the Sedevacantists can quibble until you're blue in the face regarding "That would have been infallbile [had they been legitimate popes]. No it wouldn't. Yes it would."
ad infinitum, ad nauseamBoth sides are missing the forest of indefectibility for the trees of infallibility. If all that had happened in the 1960s were a few ambiguous or even erroneous statements in Vatican II, and no New Mass, no clown "Masses", no female eucharistic ministers, altar girls, "communion" in the hand, etc. ... there WOULD NOT HAVE BEEN A TRADITIONAL MOVEMENT.
While the R&R interpretation regarding the notes of infallibility is absurdly narrow, the simple fact is that there had been some theologians after Vatican II who held a similarly narrow view, and who had not been condemned. In fact, you'll not be able to find a single one who extended the scope of infallibility to the almost absurd lengths that the SVs have.
But that's the wrong problem, and it will not be resolved here.
What's at issue is that if you have decided that things are so bad in the Conciliar Church that you are required in conscience, to avoid offending God, and to save your soul ... to severe communion with the "Church", that you can't join them in their official public worship of God, or accept their Canon Law (where non-Catholics can receive the Sacraments), or accept their bogus cultus (i.e the bogus canonizations), since it's the very mission of the Church to guide souls in the truth and toward the sanctification of their souls, you're positing the defection of the Church in her mission to save souls. Period. End of story.
If you believe that the conditions in the Conciliar Church are accidental to the Conciliar Church, rather than being a substantial break, then you'd best get your rear end back over to one of the "Ecclesia Dei" groups or to join the Eastern Rites, or whatever. But if they're substantial, where the Conciliar Religion represents a substantial rupture from the Catholic Church of all times, then considering that to be the Catholic Church would be both heretical and blasphemous. You have to pick.