Leo XIII:
I pray . . . that they all may be one, as Thou Father in Me, and I in Thee: that they also may be one in Us. And as this Divine Prayer and Supplication does not include only the souls who then believed in Jesus Christ, but also every one of those who were henceforth to believe in Him, this Prayer holds out to Us no indifferent reason for confidently expressing Our hopes, and for making all possible endeavors in order that the men of every race and clime should be called and moved to embrace the Unity of Divine Faith.
Exact same thing. It's clear you reject the traditional understanding of this prayer.
A basic understanding of the encyclical tells one easily that JPII does not hold that the prayer of the Lord was not fulfilled in the unity of the Catholic Church.
A basic ability to read tells you that he does.
Jesus himself, at the hour of his Passion, prayed "that they may all be one" (Jn 17:21). This unity, which the Lord has bestowed on his Church and in which he wishes to embrace all people, is not something added on, but stands at the very heart of Christ's mission. (UUS 9)
This is more of JPII's effort to find a way to prove universal salvation.
JPII teaches explicitly that universal salvation is false.
Let me take this occasion to clarify a further point. I reported that Pope John Paul II, according to the English text of one of his General Audience talks, said: “Eternal damnation remains a possibility, but we are not granted, without special divine revelation, the knowledge of whether or which human beings are effectively involved in it.” By now I have been able to get my hands on the official (Italian) version of the talk in the Insegnamenti di Giovanni Paolo II. It agrees with the English except that the words “whether or” are omitted. Thus the Pope cannot be cited as tending toward universalism. On the contrary, he teaches here as elsewhere that some have in fact said “no” to the divine invitation to everlasting life. (Avery Cardinal Dulles, First Things, October 2003, Reply to Correspondence)
But the problem remains. Can God, who has loved man so much, permit the man who rejects Him to be condemned to eternal torment? And yet, the words of Christ are unequivocal. In Matthew's Gospel He speaks clearly of those who will go to eternal punishment (cf. Mt 25:46). Who will these be? The Church has never made any pronouncement in this regard. (John Paul II, Crossing the Threshold of Hope, Chapter 28)
What problem is JPII referring to in Crossing the Threshold of Hope?
Wishful thinking on your part: Leo never implies and it can't be inferred that the prayer of Our Lord lacks fulfillment. From the same letter: "To complete the harmony of this most desired unity, it remains for Us to address all those throughout the world whose salvation has long been the object of Our thoughts and watchful cares; We mean Catholics, whom the profession of the Roman faith, while it renders them obedient to the Apostolic See, preserves in union with Jesus Christ. There is no need to exhort them to true and holy unity, since through the divine goodness they already possess it; nevertheless, they must be admonished, lest under pressure of the growing perils on all sides around them, through negligence or indolence they should lose this great blessing of God.
Leo also throughout the entire letter unambiguously makes known the absolute necessity of all "christians" to return to the Catholic Church and submit to the Roman Pontiff in order to secure their salvation. It is only in the Catholic Church that Ut Unum Sint as the prayer of Our Lord is fulfilled. Those who separate from that unity do not invalidate the prayer of Our Lord. They simply make a shipwreck of their faith and ruin their chance of salvation.