As I understand Catholic eschatology, you have misplaced the reign of peace in the chronology.

Luke 18

20 And being asked by the Pharisees, when the kingdom of God should come? he answered them, and said: The kingdom of God cometh not with observation:

21 Neither shall they say: Behold here, or behold there. For lo, the kingdom of God is within you.  22 And he said to his disciples: The days will come, when you shall desire to see one day of the Son of man; and you shall not see it.  23 And they will say to you: See here, and see there. Go ye not after, nor follow them:  24 For as the lightning that lighteneth from under heaven, shineth unto the parts that are under heaven, so shall the Son of man be in his day.  25 But first he must suffer many things, and be rejected by this generation.

26 And as it came to pass in the days of Noe, so shall it be also in the days of the Son of man.  27 They did eat and drink, they married wives, and were given in marriage, until the day that Noe entered into the ark: and the flood came and destroyed them all.  28 Likewise as it came to pass, in the days of Lot: they did eat and drink, they bought and sold, they planted and built.  29 And in the day that Lot went out of Sodom, it rained fire and brimstone from heaven, and destroyed them all.  30 Even thus shall it be in the day when the Son of man shall be revealed.

31 In that hour, he that shall be on the housetop, and his goods in the house, let him not go down to take them away: and he that shall be in the field, in like manner, let him not return back.  32 Remember Lot's wife.  33 Whosoever shall seek to save his life, shall lose it: and whosoever shall lose it, shall preserve it.  34 I say to you: in that night there shall be two men in one bed; the one shall be taken, and the other shall be left.  35 Two women shall be grinding together: the one shall be taken, and the other shall be left: two men shall be in the field; the one shall be taken, and the other shall be left.

36 They answering, say to him: Where, Lord?  37 Who said to them: Wheresoever the body shall be, thither will the eagles also be gathered together.

Acts 1

6 They therefore who were come together, asked him, saying: Lord, wilt thou at this time restore again the kingdom to Israel?  7 But he said to them: It is not for you to know the times or moments, which the Father hath put in his own power:  8 But you shall receive the power of the Holy Ghost coming upon you, and you shall be witnesses unto me in Jerusalem, and in all Judea, and Samaria, and even to the uttermost part of the earth.  9 And when he had said these things, while they looked on, he was raised up: and a cloud received him out of their sight.  10 And while they were beholding him going up to heaven, behold two men stood by them in white garments.


11 Who also said: Ye men of Galilee, why stand you looking up to heaven? This Jesus who is taken up from you into heaven, shall so come, as you have seen him going into heaven.

Romans 11

 25 For I would not have you ignorant, brethren, of this mystery, (lest you should be wise in your own conceits), that blindness in part has happened in Israel, until the fulness of the Gentiles should come in. 26  And so all Israel should be saved, as it is written: There shall come out of Sion, he that shall deliver, and shall turn away ungodliness from Jacob

Catholic Public Domain Version

And in this way, all of Israel may be saved, just as it was written: “From Zion shall arrive he who delivers, and he shall turn impiety away from Jacob.

New American Bible

and thus all Israel will be saved, as it is written: “The deliverer will come out of Zion, he will turn away godlessness from Jacob;

New International Version

and in this way all Israel will be saved. As it is written: “The deliverer will come from Zion; he will turn godlessness away from Jacob.

English Standard Version

And in this way all Israel will be saved, as it is written, “The Deliverer will come from Zion, he will banish ungodliness from Jacob”;

Contemporary English Version

In this way all of Israel will be saved, as the Scriptures say, "From Zion someone will come to rescue us. Then Jacob's descendants will stop being evil.

Good News Translation

And this is how all Israel will be saved. As the scripture says, "The Savior will come from Zion and remove all wickedness from the descendants of Jacob.

21 Tell me, you that desire to be under the law, have you not read the law?  22 For it is written that Abraham had two sons: the one by a bondwoman, and the other by a free woman.  23 But he who was of the bondwoman, was born according to the flesh: but he of the free woman, was by promise.  24 Which things are said by an allegory. For these are the two testaments. The one from mount Sina, engendering unto bondage; which is Agar:  25 For Sina is a mountain in Arabia, which hath affinity to that Jerusalem which now is, and is in bondage with her children.


26 But that Jerusalem, which is above, is free: which is our mother.  27 For it is written: Rejoice, thou barren, that bearest not: break forth and cry, thou that travailest not: for many are the children of the desolate, more than of her that hath a husband.  28 Now we, brethren, as Isaac was, are the children of promise.  29 But as then he, that was born according to the flesh, persecuted him that was after the spirit; so also it is now.  30 But what saith the scripture? Cast out the bondwoman and her son; for the son of the bondwoman shall not be heir with the son of the free woman.

31 So then, brethren, we are not the children of the bondwoman, but of the free: by the freedom wherewith Christ has made us free.

Good Heavens. Please be precise.

Are you saying that in The End every single remaining Jєω is the "remnant" that will be saved?

I am reasonably knowledgeable about Jєωs and about The End. I have never seen anyone (except the heretic josh987654321), Magisterial or otherwise, claim that every single Jєω alive on The Last Day will convert. Everything Magisterial that I have read teaches that from Christ's Ministry until The Last Day a remnant will be saved—here and there, as it were, NOT here and there until The Last Day and then on the Last Day every single one will convert. I have never seen such a bizarre and qualified teaching from the Magisterium. If you have it, let's see it. Not speculation, but Magisterium!

If you have Magisterium saying that every single Jєω alive on The Last Day will convert, I would submit to authentic Magisterium and, if I have been wrong, I will abjure my error.

I'll add this. There is virtual unanimity among the Fathers that The Anti-Christ will be a Jєω and that he will be destroyed, not converted, on The Last Day.  That would certainly be at least one Jєω of the remnant left alive on The Last Day who did not convert, but damned instead. To me, that one exception alone makes the "every single one on The Last Day"  claim to be an absurd, untenable, and heretical claim.

His acknowledgment of exceptions means "not every single Jєω" alive on The Last Day will convert to Christ.

I am at a disadvantage because (1) as I said before, I make no claim of being expert on eschatology and (2) almost my entire Judaica library is boxed in preparation to move. All I have at hand is what is on my computer. What is there to misunderstand about "only a remnant will be saved"? Your claim of "interpretation" seems of the same species as Bill Clinton's "What is the meaning of 'is'?"

I have attached the best compendium I have at hand. The screen shots of the Table of Contents show that almost every aspect of the mass conversion claim and the claimants is covered comprehensively. As the subtitle states, the compendium was prepared to rebut the claims of Fr. Mawdsley who has been quoted here.

For those who struggle to find any excuse to avoid reading or challenging the Magisterial evidence adduced, I am sure they will contrive some animus against the author (as when I introduced Hoffman's book) or complain that there is no imprimatur (as we have also seen recently). For that ilk, "Any excuse is better than no excuse," eh?

The file can be download below.

I am at a disadvantage because (1) as I said before, I make no claim of being expert on eschatology and (2) almost my entire Judaica library is boxed in preparation to move. All I have at hand is what is on my computer. What is there to misunderstand about "only a remnant will be saved"? Your claim of "interpretation" seems of the same species as Bill Clinton's "What is the meaning of 'is'?"

I have attached the best compendium I have at hand. The screen shots of the Table of Contents show that almost every aspect of the mass conversion claim and the claimants is covered comprehensively. As the subtitle states, the compendium was prepared to rebut the claims of Fr. Mawdsley who has been quoted here.

For those who struggle to find any excuse to avoid reading or challenging the Magisterial evidence adduced, I am sure they will contrive some animus against the author (as when I introduced Hoffman's book) or complain that there is no imprimatur (as we have also seen recently). For that ilk, "Any excuse is better than no excuse," eh?

The file can be download below.

4.  The Church Fathers are the ones who, taking St Paul's words in Scripture, taught that the Jєωιѕн Nation will convert before the Last Day.

An impressive list of Fathers can be brought out who refer to this future conversion as a fact. Included are Tertullian, Origen, Saint Hilary, Saint Ambrose, Saint John Chrysostom, Saint Jerome, Saint Cyril of Alexandria, Saint Prosper of Aquitaine, Saint Gregory the Great, Saint Isidore, Saint Bede the Venerable, and Saint Anselm. Saint Cyril of Alexandria says this: “Towards the end of time, Our Lord Jesus Christ will effect the reconciliation of His former persecutor Israel with Himself. Everybody who knows Holy Scripture is aware that, in the course of time, this people will return to the love of Christ by the submission of faith…. Yes, one day, after the conversion of the Gentiles, Israel will be converted, and the Jews will be astonished at the treasure they will find in Christ” (Commentary on Genesis, Bk. 5).

https://catholicism.org/ad-rem-no-310.html

"And Isaias crieth out concerning Israel: If the number of the children of Israel be as the sand of the sea, a remnant shall be saved. (Romans 9:27)
 
"Even so then at this present time also, there is a remnant saved according to the election of grace." (Romans 11:5)