The New Heaven and New Earth is the end of the story for the non-reprobate. This is after the disembodied souls enter the beatific vision. This is when those disembodied souls are united with their glorified bodies at the General Judgement.

And The New Heaven and New Earth occurs when Heaven comes down and merges with Earth. Apocalypse 21:

1 And I saw a new heaven and a new earth. For the first heaven and the first earth was gone, and the sea is now no more.  2 And I John saw the holy city, the new Jerusalem, coming down out of heaven from God, prepared as a bride adorned for her husband.  3 And I heard a great voice from the throne, saying: Behold the tabernacle of God with men, and he will dwell with them. And they shall be his people; and God himself with them shall be their God.  4 And God shall wipe away all tears from their eyes: and death shall be no more, nor mourning, nor crying, nor sorrow shall be any more, for the former things are passed away.  5 And he that sat on the throne, said: Behold, I make all things new.

This is right after the General Judgement. After the GJ, the people in "Limbo" (or whatever you want to call it) will enter the NHNE as well. They do not go to eternal Hell. And there are only two abodes after the GJ: the Kingdom of God and the Kingdom of Satan.

OK, so here you completely trip yourself up.  Those in Limbo are NOT PUNISHED, and those in Limbo HAVE NOT LOST GOD simpliciter.  They do not receive the Beatific Vision, which is a free gift of God, which our created nature can't begin to comprehend, as it's beyond the capacity of our nature, but in no way is deprivation of the Beatific Vision a punishment  This is what St. Thomas articulated regarding Limbo, and it's also what Pope Pius IX was talking about in terms of how God will not permit those who have not committed actual sin to be punished.  St. Gregory nαzιanzen, in those passage you should know quite well, since it's where he rejects Baptism of Desire, talks about how there are those who are not bad enough to be punished, but not good enough to be glorified, glorification being the elevation of our nature to where we can see God face to face.

Hell is where the enemies of God go, the reprobate, but the infants in Limbo are not reprobate, are not being punished, are perfectly happy, are not in any enmity with God, and they undoubtedly interract with the saints who are in fact able to behold the Beatific Vision, something which the damned would not and cannot do.

You're stuck in the very same binary mindset of how there's only Heaven (with the Beatific Vision) or else Hell (with punishments), and it's why St. Augustine concluded that infants who die without Baptism are punished ... although just a little bit, on account of their loss of God.  St. Thomas helped overturn this binary thinking and articulated the distinction between the supernatural elevation of Heaven, and the natural reward vs. punishment.

So, unhappiness and suffering are the results of being deprived of a due good.  But because human nature does not even have a capacity to see God face to face and enjoy the Beatific Vision, the simple lack of the Beatific Vision along cannot cause suffering.  By way of analogy, a squirrel does not suffer because it lacks the capability of speech, and that's because it has no clue even what that is, and its nature was not designed in such a way that the squirrel's perfection requires the faculty of speech, and therefore the lack of something that it hasn't even got the capacity for cannot cause suffering.

• Justification: God desires that all men avoid all punishment and deprivation of His presence. The fact that outcomes fall short of this desire (resulting in Limbo, Purgatory, or Hell) is due to human free will and the failure to cooperate fully with the means of grace, not a limitation in God’s desire for the ultimate good of His children.

• Conclusion: The Church is necessary because it is the only guaranteed path to remove the barrier of Original Sin, ensure the highest intermediate reward (Beatific Vision), and provide the essential graces that protect the soul from the mortal sin that leads to eternal damnation.

This is interesting, and I suppose we are free to speculate about NHNE (within reason)

However, something that immediately comes to mind is that that these infants, and the "invincibly ignorant", still have Original Sin. This synopsis gives no reason as to why or how Original Sin will be able to be present in NHNE.

Right, but as Original Sin is an impediment to the Beatific Vision, and as we know that the Old Testament Just now enjoy the Beatific Vision, it obviously follows that they were delivered from that state of sin by Our Lord's Passion. That is why they could only enter Heaven after It had occurred

So the synopsis is implying that the infants who die in original sin, and those invincibly ignorant, will have Original Sin remitted at the General Judgement?

"Do not marvel at this; for an hour is coming, in which all who are in the tombs will hear His voice, and will come forth; those who did the good deeds to a resurrection of life, those who committed the evil deeds to a resurrection of judgment."


— John 5:28–29

"For the Lord Himself will descend from heaven with a shout, with the voice of the archangel and with the trumpet of God, and the dead in Christ will rise first. Then we who are alive and remain will be caught up together with them in the clouds to meet the Lord in the air, and so we shall always be with the Lord."

• 1 Corinthians 15:52: This highlights the speed and finality of the transformation at the last trumpet.

"In a moment, in the twinkling of an eye, at the last trumpet; for the trumpet will sound, and the dead will be raised imperishable, and we will be changed."

So will the infants and those invincibly ignorant who die with Original Sin on their souls be able to enter NHNE with Original Sin, or will those with the guilt of Original Sin on their souls be remitted of it at Christ's Second Coming