You are right to say that the Catholic Church has always taught that conversion to the Catholic Church is necessary for true ecumenism. But you are wrong to say that since the advent of the Second Vatican Council the mission has ceased. Nor is it true that Catholics are now taught that the Catholic Church is simply one of many paths to God.
The Fathers of the Second Vatican Council explicitly taught that “God himself has made known to mankind the way in which men are to serve Him, and thus be saved in Christ and come to blessedness. We believe that this one true religion subsists in the Catholic and Apostolic Church, to which the Lord Jesus committed the duty of spreading it abroad among all men.” (Dignitatis humanae, 1.) On false ecumenism and evangelization, Vatican II’s Decree on Ecumenism (Unitatis Redintegratio) says the following “Nothing is so foreign to the spirit of ecumenism as a false irenicism, in which the purity of Catholic doctrine suffers loss and its genuine and certain meaning is clouded. At the same time, the Catholic faith must be explained more profoundly and precisely, in such a way and in such terms as our separated brethren can also really understand.”
Of course the Church acknowledges that many truths are found in other ecclesial communities, but Pope John Paul II warns: “The Christian faithful are therefore not permitted to imagine that the Church of Christ is nothing more than a collection—divided, yet in some way one—of Churches and ecclesial communities; nor are they free to hold that today the Church of Christ nowhere really exists, and must be considered only as a goal which all Churches and ecclesial communities must strive to reach.” (*Dominus Iesus * no.16)
The Holy Father goes on to say say that “the Second Vatican Council sought to harmonize two doctrinal statements: on the one hand, that the Church of Christ, despite the divisions which exist among Christians, continues to exist fully only in the Catholic Church, and on the other hand, that “outside of her structure, many elements can be found of sanctification and truth”, that is, in those Churches and ecclesial communities which are not yet in full communion with the Catholic Church. But with respect to these, it needs to be stated that “they derive their efficacy from the very fullness of grace and truth entrusted to the Catholic Church”. (ibid).
Those who don’t abide in the fullness of grace and truth entrusted to the Catholic Church need to be evangelized. The Church needs you to evangelize! Share your love and knowledge of the faith with others. Also pray for those Catholics who know and love their faith that the Holy Spirit will help them to continually grow in their understanding of the Church’s teachings so they can witness more effectively. As Pope John Paul II said, “Woe to me if I do not evangelize.”
On the subject of ecumenism, I recommend you read the following: Unitatis Redintegratio, Gaudium et Spes, Dominus Iesus, Dignitatis humanae, and *The Splendor of Truth * by Pope John Paul II.