Catholics believe we are judged immediately after we die (Particular Judgement). Some of us will go to heaven. Then there is still the Last Judgement (or Final Judgement).
Two important things will happen to us at the last judgment that were not already done at our particular judgment. First, although our souls will already have gone to heaven (possibly via purgatory) or to hell, at the last judgment our bodies will be reunited with our souls, to join in their joy or suffering. Second, the last judgment will be public, seen and understood by the whole world, whereas our particular judgment was private, just between God and ourselves. At the last judgment, everyone will see how each of us has cooperated or failed to cooperate with the graces God has given us. Both God's mercy and His justice will be visible to all, and even those who, in this life, worry about how a good God can condemn anyone to hell forever will see that those condemnations are entirely appropriate.
This is as close as I can get. I do not have a degree in theology only ministry which is quite different.
AKA Already judged and rewarded.
>>or to hell,<<<
AKA Already judged and in punishment.
Matthew 25 and He will separate people one from another as a shepherd separates his sheep from the goats,
According to your hypothesis that has already been done. Why does He need to do it again?
>>Second, the last judgment will be public, seen and understood by the whole world, whereas our particular judgment was private, just between God and ourselves.<<
That doesn't fit with your hypothesis. Catholics claim those saved are already in heaven and know all that's going on here on earth. If you know Mary and the saints are in heave how is that private?
Your entire scenario contradicts what Catholics say they believe about people alive in heaven already who know what is happening here on earth and can intervene. And if unbelievers are already suffering in hell they have obviously been judged and told why they are in hell.
I know you stated you are not a theologian, neither am I but familiar with some of the Church history with regards to your statement above. "Cooperating" with the graces of God is a semi-pelagian construct. Here is some information on the subject:
Council of Orange: was called by Pope Felix IV in 529 A.D
The Council approved the Augustinian doctrine of sin and grace over against what would be called Semi-Pelagianism, but without Augustine's absolute predestination. The Canons of the Council of Orange constitute the judgement of the Council.
"Humanism, in all its subtle forms, recapitulates the unvarnished Pelagianism against which Augustine struggled. Though Pelagius was condemned as a heretic by Rome, and its modified form, Semi-Pelagianism was likewise condemned by the Council of Orange in 529, the basic assumptions of this view persisted throughout church history to reappear in Medieval Catholicism, Renaissance Humanism, Socinianism, Arminianism, and modern Liberalism." R. C. Sproul(http://www.theopedia.com/Council_of_Orange)
More:
Semi-Pelagianism is a weaker form of Pelagianism (a heresy derived from Pelagius who lived in the 5th century A.D. and was a teacher in Rome). Semi-Pelagianism (advocated by Cassian at Marseilles, 5th Century) did not deny original sin and its effects upon the human soul and will; but, it taught that God and man cooperate to achieve man's salvation. This cooperation is not by human effort as in keeping the law but rather in the ability of a person to make a free will choice. The semi-Pelagian teaches that man can make the first move toward God by seeking God out of his own free will, and that man can cooperate with God's grace even to the keeping of his faith through human effort. This would mean that God responds to the initial effort of person, and that God's grace is not absolutely necessary to maintain faith.
The problem is that this is no longer grace. Grace is the completely unmerited and freely given favor of God upon the sinner; but, if man is the one who first seeks God, then God is responding to the good effort of seeking him. This would mean that God is offering a proper response to the initial effort of man. This is not grace but what is due the person who chooses to believe in God apart from God's initial effort.
• Semi-Pelagianism says the sinner has the ability to initiate belief in God.
• Semi-Pelagianism says God's grace is a response to man's initial effort.
• Semi-Pelagianism denies predestination.
Semi-Pelagianism was condemned at the Council of Orange in 529.(http://carm.org/semi-pelagianism)