I agree that Vatican II must be seen in the light of tradition, but the change in the No Salvation teaching occurred way before Vatican II.
In his encyclical Quanto conficiamur moerore, 1863, Pius IX said:
It is known to us and to you that those who are in invincible ignorance of our most holy religion, but who observe carefully the natural law, and the precepts graven by God upon the hearts of all men, and who being disposed to obey God lead an honest and upright life, may, aided by the light of divine grace, attain to eternal life; for God who sees clearly, searches and knows the heart, the disposition, the thoughts and intentions of each, in His supreme mercy and goodness by no means permits that anyone suffer eternal punishment, who has not of his own free will fallen into sin.
Again, contrast with:
◦“The most Holy Roman Church firmly believes, professes and preaches that none of those existing outside the Catholic Church, not only pagans, but also Jews and heretics and schismatics, can have a share in life eternal; but that they will go into the eternal fire which was prepared for the devil and his angels, unless before death they are joined with Her; and that so important is the unity of this ecclesiastical body that only those remaining within this unity can profit by the sacraments of the Church unto salvation, and they alone can receive an eternal recompense for their fasts, their almsgivings, their other works of Christian piety and the duties of a Christian soldier. No one, let his almsgiving be as great as it may, no one, even if he pour out his blood for the Name of Christ, can be saved, unless he remain within the bosom and the unity of the Catholic Church.” (Pope Eugene IV, the Bull Cantate Domino, 1441.)