If only the SSPX truly promoted the idea that the Pope Question must be left up to God. For the most part and in practice, they assert and proclaim that it's not Catholic to even have questions and doubts--despite the fact that Archbishop Lefebvre himself expressed such doubts in public and tolerated sedevacantist-like questioning. Part of it may be politics, part a reaction against the excesses of the sedevacantists. Bishop Williamson has recently told someone I know that the only hope to save the Church would be through diplomacy. When I was at seminary about 20 years ago, he consistently said that the only resolution would be an act of divine intervention.
Unfortunately, the implicit SSPX position entails believing in a Pope and a Church which can promulgate a bastard Protestantized Mass which Catholics cannot attend in good conscience and without harm to their faith. Every theologian before Vatican II would have denounced as a heretic anyone who held this proposition.
Now, of course there's no monolithic SSPX, and there are shades of thinking privately among the SSPX priests. But this at least implicit position is the reason why there's a constant movement of people, priests and faithful, to the right and to the left, as it were--in order to resolve this conflict and contradiction. If these men are popes, we have to accept the New Mass as at least legitimate and sanctifying in and of itself. If we have to reject the New Mass, then we have to reject the Popes who promote and promulgate it.
One could argue that the NO Mass is not inherently inimical to the Faith. If you look at the Latin version, follow various rubrics and customs, etc.--such as when they do it in Latin on EWTN--it suddenly doesn't seem so bad. Is there something inherently un-Catholic about reducing the number of Kyrie/Christe eleisons from 9 to 3?
There are a number of arguments one can make such as that the NO Church never formally mandated the New Mass, the V2 was a pastoral Council, etc.--but this would be to reduce the Church's infallibility to a matter of subtle legal technicalities.
So I think that the official position should be one of DOUBT, of publicly expressed DOUBT. SSPX should come out and state that these popes are doubtful. As canon lawyers declare, one cannot be guilty of schism if he entertains doubts about the person of the pope based on widespread and widely known factors. And this public stance by the SSPX would set into motion a set of events that could eventually lead to a resolution of the crisis.
So the SSPX has created a serious theological problem--essentially upholding a papacy of honor only, where you stick a picture of the pope in your chapels' vestibule and otherwise complete ignore him, blow him off, and pretend he doesn't exist--for all intents and purposes.
As I've argued, however, sedevacantism has its own issues, undermining the magisterium itself by allowing the vacancy of the Holy See or its occupancy to be ultimately subjected to private judgment. So we have to prescind from making this judgment--in order to defer to the Church's authority.
If I were a priest, I would offer Mass una cuм famulo tuo papa nostro [without the name], thus expressing my doubt about the person without making a definitive judgment of sedevacante.
There's a lot of bad theology in the SSPX: the Catholic Church vs. the official Church, eternal Rome vs. modernist Rome, "faith is greater than obedience" (does not apply here), validity of Confessions due to "common error", etc. And once seminarians start studying traditional dogmatic theology, the contrast between what's in those books and some of the SSPX theological lines becomes apparent.
So they end up running to the other excess of dogmatic sedevacantism. I spent hours and hours discussing sedevacantism with Bishop Williamson, and none of his reponses to the theological problems I had were at all convincing. They were poetic and quasi-mystical rather than theological. Now, had he brought up the reduction ad absurdum arguments which God later brought to my mind, I probably would have stayed. I really really, desperately, did NOT want to leave. I was looking for something, anything, that would have enabled me to stay in good conscience. I got nothing.