I always doubted that the SSPX leadership was that serious in insisting that Rome returns "to the True Faith". It was always eagerly waiting to embrace the devils in Rome if the practical terms were right. To some extent trad Catholics were duped into thinking the Society had firm policies when all the time it was and is wandering all over the place. ABL wanted to corner the market and suck in big money for his particular 'experiment of tradition' and so played to many different audiences. To say that his was the only game in town undermines the capacity of the trad movement to respond effectively to Rome's defection and leaves it to vacillating bishops and teams of groupie priests to fill the huge vacuum.
There is an open letter that was first printed in Culture Wars Magazine entitled,
Why the SSPX Cannot Effectively Defend Catholic Tradition. Its point was that Archbishop Lefebvre failed to defend two absolutely essential points: The immutability of Catholic Dogma, and the Immemorial Roman rite of Mass as necessary attribute of the Catholic Faith and not a simple matter of Church discipline. +Lefebvre held that any "good" Muslim, Hindu, Jew, Buddhist, Protestant, Orthodox, etc. could gain eternal salvation by being a "good" Muslim, Hindu, Jew, Buddhist, Protestant, Orthodox, etc. He held that the dogma of faith that there is 'no salvation outside the Catholic Church' was dispensed by "invincible ignorance." This means that dogma (in the category of Truth-Falsehood) , which are truths infallibly defined as formal objects of divine and Catholic Faith, could be treated in the same manner as laws, commands, injunctions, directives, counsels, etc. (in the category of Authority-Obedience), which do not bind in the cases of impossibility, undue burden or hardship. Thus truth can be dispensed with.
The other serious problem was that he held that the liturgy was a matter of pure Church discipline open to the free will of the legislator to do as he pleased. His only objection was that the legislator could not introduce anything "harmful to the faith" and he made himself the judge as to what was "harmful." Thus the idea of liturgical experts and liturgical committees were acceptable to him. +Lefebvre accepted all the liturgical changes until about 1965 as well as some beyond that. It is reported that he concelebrated the Novus Ordo in the early 70s at his sisters funeral. It was not until 1983 that he adopted the 1962 Bugnini liturgical books for the SSPX. He offered no appeal to the dogmas of Catholic Faith on the authority of Ecclesiastical Tradition or from the dogma from the Council of Trent defending the "received and approved" rites of the Church. He never rejected completely the treatment of the 1962 Missal as an Indult as being unheard of and impossible impositions against an immemorial tradition.
What should be remembered is that +Lefebvre was a late comer to the defense of the Catholic tradition. Fr. Gommar DePauw, a peritus at Vatican II, was active before +Lefebvre and so was Fr. Francis Fenton and the ORCM which established traditional Mass centers. When the SSPX came to the U.S. they established their Mass centers in competition with other traditional Masses in a direct effort to put them out of business arguing that they had a bishop thus only they could provide all the sacraments. That is exactly what the Fraternity of St. Peter did after 1988 against the SSPX. +Lefebvre never offered to ordain priests for any organization that he did not control and part of his control required the acceptance of his positions on the nature of dogma and liturgy. Bishop Fellay has continued in the same manner. Even the nine priests who left the SSPX in 1983 took these two pieces of baggage with them.
A sedevancantist bishop once suggested to me that +Lefebvre may have been an agent provocateur. That he actively worked to destroyed any opposition to modernist Rome that he did not control while forming his opposition on first principles that would ultimately be indefensible and collapse.
I did not agree and still do not think so. I think +Lefebvre had made many compromises with regard to dogma and liturgy before he saw the danger. Once seeing the danger he did not address these fundamental errors in his thinking and he tried to apply outdated forms of opposition that could not work.
+Williamson will not be able to help unless a new approach is taken. IMO he should ordain priests and consecrate bishops for any group or organization that will defend the immutability of dogma and the fundamental right of every Catholic Faithful to the "received and approved" rites of the Catholic Church. Guerrilla warfare should be the strategic model in a loose confederation without any central command. Traditional Catholics should not try to create a parallel Church with a set consolidated hierarchical structure in opposition, but small diffused groups that can maintain a permanent resident priest in opposition to their local ordinaries. The formation of priests will also need a different approach and there are many historical models that should be considered. The internet would be a big help in making earlier models more successful for education of priests today and social networks could also be used for this purpose.