I may be remembering incorrectly, but I believe that this information is not accurate:
"... Vatican II as infallible on faith and morals."
During the time of Vatican II I was blessed to be in seminary. It was an exciting time and it was most interesting to hear about events and teachings from various experts and bishops who were directly involved in the Council.
One thing that I heard frequently was that the Fathers of Vatican II were influenced by Eastern Christian teaching on the nature of the Church as a Communion of Churches. This made eminent good sense since one function of the Second Vatican Council was to complete the work of Vatican I on the role of the papacy among the Churches. Vatican I was ended before its work was completed by the invasion and loss of the Vatican States. (Some have said that it was Providentially ended in light of Vatican II.)
What better way to start the work of finishing the teachings of Vatican I than to place them in the context of what makes Church to be Church?
If I remember correctly we were taught that the Council Fathers of Vatican II explicitly refused to invoke the teaching of infallibility when issuing their teachings. The teaching on infallibility was placed squarely in the context of the working of the Spirit in the church to let us know what reality is.
So, if infallibility was to be asserted for the teachings of Vatican II, it was not done formally as under the expression that rose from Vatican I. If I remember the Fathers consciously chose not to invoke Counciliar or Papal infallibility in Vatican I terms to authenticate their teaching. They chose not to so that they could reinforce the doctrine that it is the Church which is infused with the gift of infallibility and that infallibility is expressed in a number of ways.
I'm not sure that this adds much to the discussion in this thread, but I think the teaching on infallibility is much richer for Vatican II which puts Papal Infallibility in the context of Church as communion of Churches.
Certainly, as our brothers and sisters who are Orthodox and Orthodox in Communion with Rome remind us in the West, we do not yet share a complete understanding of infallibility in the Church or how it should function. Even Pope John Paul II intimated as much. He invited our Eastern brothers and sisters to join us in exploring the charism inherent in his role as servant among the churches for example.
Again, if I recall correctly, we were taught that it was a service of love in the ideal. Its focus was not power; it was service.
I think it would be fascinating to hear the leaders and theologians and faithful of the Churches describe what a servant of the servants of God is in the language of love and service. That might begin to make the discussion like the one with the Lefebvrites and others inviting to non believers. Maybe they could judge us as guilty of loving one another even in our dissention.
Steve