The Church of Christ

Is it true as many Traditional Catholics have purported that Vatican II ecclesiology changed the definition of the Church of Christ--which for almost 2000 years was said to be identical with the Roman Catholic Church--to a much more broad entity made up of many ecclesial communities of which the Roman Catholic Church is but one among many albeit perhaps the most historical and complete? Does the Church of Christ only "subsist" in the Roman Catholic Church to utilize Conciliar terminology e.g. Unitatis Redintegratio, no. 4 and Lumen Gentium, no. 8, 21, Nov. 1964, Vatican II for example?

To put a finer point on this question; does the Roman Catholic Church exist (as a discreet current or stream might flow) in a much larger "river" of "water" which is the Church of Christ? Moreover, what are we to make of the fact that the other "ecclesial communities" are said to possess salvific character as entities--meaning that one can be saved by being a member in good standing of these communities? How is this to be harmonized with the constant Magisterial teaching: Extra Ecclesium Nulla Sullus (outside the Roman Catholic Church there is no salvation) as repeatedly expressed by pre-Vatican II Papal Bulls (Ex-Cathedra pronouncements) and constant Magisterial teaching?

If such a change has really been made would it not violate the law of non-contradiction, i.e. if the Church of Christ is identical with the Roman Catholic Church in submission to the Roman Pontiff it cannot include any other if words are to have any meaning? Moreover, if such a change has actually been made, would it not violate Sacred Tradition which dates to the time of the Church Fathers and Jesus Christ himself?

One can understand the desire that the Fathers of the Second Vatican Council surely had in wishing to recognize the good found in many individual non-Catholic persons and the truth which they posses, albeit incomplete. Yet, would it not be more consistent with Sacred Tradition and constant Magisterial teaching to say that--since God alone knows the heart and disposition of every person who ever lived, HE may find that-- certain members of various non-Roman Catholic ecclesial communities may through invinsible ignorance be saved, but the communities themselves do not and cannot possess salvific character without violating Sacred Tradition?