How do Roman Catholics explain their change in Eschatology?
In the body of your question, you have not established nor stated what is the particular change that you are referring to, so there is no direct answer on this. The only way is to enlighten you what the Catholic eschatology means and what the Catechism of the Catholic Church teaches on eschatology.
For example see the Catholic Encyclopedia (eschatology).
In this article there is no critical discussion of New Testament eschatology nor any attempt to trace the historical developments of Catholic teaching from Scriptural and traditional data; only a brief conspectus is given of the developed Catholic system. For critical and historical details and for the refutation of opposing views the reader is referred to the special articles dealing with the various doctrines.
Escahatology as explain in the Catechism of the Catholic Church
"I BELIEVE IN LIFE EVERLASTING"
1020 The Christian who unites his own death to that of Jesus views it as a step towards him and an entrance into everlasting life. When the Church for the last time speaks Christ's words of pardon and absolution over the dying Christian, seals him for the last time with a strengthening anointing, and gives him Christ in viaticum as nourishment for the journey, she speaks with gentle assurance:
I. THE PARTICULAR JUDGMENT
1021 Death puts an end to human life as the time open to either accepting or rejecting the divine grace manifested in Christ.592 The New Testament speaks of judgment primarily in its aspect of the final encounter with Christ in his second coming, but also repeatedly affirms that each will be rewarded immediately after death in accordance with his works and faith. The parable of the poor man Lazarus and the words of Christ on the cross to the good thief, as well as other New Testament texts speak of a final destiny of the soul--a destiny which can be different for some and for others.593
1023 Those who die in God's grace and friendship and are perfectly purified live for ever with Christ. They are like God for ever, for they "see him as he is," face to face:598
III. THE FINAL PURIFICATION, OR PURGATORY
1030 All who die in God's grace and friendship, but still imperfectly purified, are indeed assured of their eternal salvation; but after death they undergo purification, so as to achieve the holiness necessary to enter the joy of heaven.
1033 We cannot be united with God unless we freely choose to love him. But we cannot love God if we sin gravely against him, against our neighbor or against ourselves: "He who does not love remains in death. Anyone who hates his brother is a murderer, and you know that no murderer has eternal life abiding in him."612 Our Lord warns us that we shall be separated from him if we fail to meet the serious needs of the poor and the little ones who are his brethren.613 To die in mortal sin without repenting and accepting God's merciful love means remaining separated from him for ever by our own free choice. This state of definitive self-exclusion from communion with God and the blessed is called "hell."
V. THE LAST JUDGMENT
1038 The resurrection of all the dead, "of both the just and the unjust,"623 will precede the Last Judgment. This will be "the hour when all who are in the tombs will hear [the Son of man's] voice and come forth, those who have done good, to the resurrection of life, and those who have done evil, to the resurrection of judgment."624 Then Christ will come "in his glory, and all the angels with him. . . . Before him will be gathered all the nations, and he will separate them one from another as a shepherd separates the sheep from the goats, and he will place the sheep at his right hand, but the goats at the left. . . . And they will go away into eternal punishment, but the righteous into eternal life."625
VI. THE HOPE OF THE NEW HEAVEN AND THE NEW EARTH
1042 At the end of time, the Kingdom of God will come in its fullness. After the universal judgment, the righteous will reign for ever with Christ, glorified in body and soul. The universe itself will be renewed:
The Church . . . will receive her perfection only in the glory of heaven, when will come the time of the renewal of all things. At that time, together with the human race, the universe itself, which is so closely related to man and which attains its destiny through him, will be perfectly re-established in Christ.631
- You had cited "Gregory I, Pope from 590-605, predicted that the end of the world was imminent in a letter he wrote to Ethelbert..."
The Catholic Church does not teaches "the end of the world" but uses the phrase "the end of time or the end of Satan reign on earth" and the entrance to the New Heaven as cited in the above Catechism.
- You also cited; "Pope Innocent III (died 1216) predicted that the world would end 666 years after the rise of Islam in 618."
This prediction is proven false, as the world continues after the year 666.
If you are looking for a credible prediction on the "end of the world or the end of Satan reign" that will leads to the Triumph of the Immaculate Heart, the article link below would be a great help for you to understand it from a Catholic perpective.
The Triumph, The Second Coming and The Eucharistic Reign
by Fr. Stefano Gobbi
June 24, 1996
Also, *Fr. Joseph Iannuzzi, O.S.J., S.T.D. In his book, “The Triumph of God’s Kingdom in the Millennium and End Times”, ia good source for you to understand eschatology based on his excellent credentials.
The Coming of Jesus and The Millennium
The subject matter in question being too complicated for me to venture into without the expertise of the masters in this field of theology, I have availed myself of the excellent research done by Fr. Joseph Iannuzzi, O.S.J., S.T.D. In his book, “The Triumph of God’s Kingdom in the Millennium and End Times”, which we have found to be the foremost authoritative work on the study of the Millennium, Fr. Iannuzzi gives a comprehensive treatise on this subject as contained in the public revelation of the Church: Sacred Scripture and Tradition (the Fathers and Doctors of the Church); and the Magisterium. It is important to note that he does not make reference in any way to private revelation to support his claims.
For more information see this link: