Yet doesn't Fr. Chazal insist that they are fully valid and true popes?
Because he has no authority to say otherwise? I think so, yes.
Where does he get the authority to reject the New Mass and VII?
At the point they break with Tradition, and, therefore place our faith in danger. Needing to determine the validity of one's office does not have an impact, one way or another, on our faith.
It's quite simple. The moment someone tells me to do something which is contrary to the Faith, I must reject it. To feel compelled to take it a step further and find out if they are what they say they are, to go out of my way to find out what the canons, theologians, et al., think is possible, when it has no real impact on my following of the Faith (as I hope I've just shown in the prior sentences is possible (and necessary) to do). His holding of his office has no bearing on my holding of my Faith then.
Bishop WIlliamson puts it much clearer, I think. (Emphasis mine):
The question is not of prime importance. If they have not been Popes, still the Catholic Faith and morals by which I must “work out my salvation in fear and trembling” (Phil. II, 12) have not changed one iota. And if they have been Popes, still I cannot obey them whenever they have departed from that Faith and those morals, because “we ought to obey God rather than men” (Acts, V, 29). However I believe in offering answers to some of the sedevacantists’ arguments, because there are sedevacantists who seem to wish to make the vacant See of Rome into a dogma which Catholics must believe. In my opinion it is no such thing. “In things doubtful, liberty” (Augustine).
What are your thoughts, my friend?