How does Catholicism biblically defend purgatory in a way that upholds the sufficiency of Christ's work? Below is a quote from an answer to this question &quot;What is the basis of the teaching that souls in purgatory can intercede for the living?:

The (Catholic) Church refers to the souls in purgatory as the Holy
Souls in Purgatory, since their salvation has been assured.,
although their souls must be purified from the remaining residue of sin committed while on earth!

From what I understand from this quote and others, the souls in purgatory are not meriting the fulfillment of their salvation by making up for sins committed but are, rather, having the sin remaining in them purged from their being much like dross is purged from precious metal.
I have seen it written in the same answer that Divine Justice is purifying souls in purgatory and we on earth can alleviate some of the pain of their waiting by our prayers and sacrifices.
My question is not about the prayers or the process of purification in purgatory.  My question is about the notion of there being some aspect of Divine Justice that was not satisfied on the sinners behalf by Jesus Christ!
If Jesus bore our sins in His body on the tree (1 Peter 2:24), and if Jesus' blood offered once for all is so much better than the blood of heifers and goats (Hebrews 9:11-15), and if Jesus' blood purifies us from all sin (1 John 1:7), and if he was delivered to death for our trespasses and raised for our justification (Romans 4:22-25), if Jesus accomplished everything that the Father sent Him to do (John 17:4) including bearing the punishment/chastisement of God that brought us peace (Isaiah 53:5),
and if we do not make peace with God by having and living out faith.  God, in Christ, has made peace with us and we enter into that rest by faith.

For in him all the fullness of God was pleased to dwell,
and through him to reconcile to himself all things, whether on earth or in heaven, making peace by the blood of his cross. - Colossians 1:19-20

How can there possibly be any remaining residue of sin left in a born again believer that Divine Justice needs to purge out that was not dealt with by the Lord Jesus Christ?  Isn't purgatory like saying that Jesus was almost successful...that He has removed only some of our sins as far as the east is from the west?
Jesus has said that He does not give peace as the world gives it (John 14:27) which is to withhold some until full reparations are made.  This is the new covenant:  &quot;Heb 8:12  For I will be merciful toward their iniquities, and I will remember their sins no more.” 
Purgatory sounds like He remembers for a while.
The Catholic Church teaches the doctrine of Purgatory while also teaching the sufficient and superabundant merits of the Passion of Christ.
The first component to understanding this is the dogma that not all temporal punishment is remitted by God with the guilt of sin and the eternal punishment. This is based upon a number of examples in Scripture where despite the guilty party being forgiven, they receive a temporal punishment for their sin. For example:

And David said to Nathan: I have sinned against the Lord. And Nathan said to David: The Lord also hath taken away thy sin: thou shalt not die. Nevertheless, because thou hast given occasion to the enemies of the Lord to blaspheme, for this thing, the child that is born to thee, shall surely die.  (2 Samuel 12:13-14)

The Church has connected this to Christ's admonition to take up your cross (do penance)

And he that taketh not up his cross, and followeth me, is not worthy of me. (Matthew 10:38)

Christ's atonement is fully adequate and superabundant:

For you are bought with a great price. ( 1 Corinthians 6:20)


Knowing that you were not redeemed with corruptible things as gold or silver, from your vain conversation of the tradition of your fathers: But with the precious blood of Christ, as of a lamb unspotted and undefiled, Foreknown indeed before the foundation of the world, but manifested in the last times for you, Who through him are faithful in God, who raised him up from the dead, and hath given him glory, that your faith and hope might be in God. (1 Peter 1:18-21)


Now the law entered in, that sin might abound. And where sin abounded, grace did more abound. (Romans 5:20)

Thus, the Church teaches that Christ's death merits sufficient grace to cover every sin, yet Divine Justice requires temporal punishment to make amends for the harm due to our sins. Our enduring temporal punishment has value because of the merits of Christ.
Finally, Purgatory as a necessity derives from Scripture:

And so betaking themselves to prayers, they besought him, that the sin which had been committed might be forgotten. But the most valiant Judas exhorted the people to keep themselves from sin, forasmuch as they saw before their eyes what had happened, because of the sins of those that were slain. And making a gathering, he sent twelve thousand drachms of silver to Jerusalem for sacrifice to be offered for the sins of the dead, thinking well and religiously concerning the resurrection, (For if he had not hoped that they that were slain should rise again, it would have seemed superfluous and vain to pray for the dead,) And because he considered that they who had fallen asleep with godliness, had great grace laid up for them. It is therefore a holy and wholesome thought to pray for the dead, that they may be loosed from sins. (2 Machabees 12:42-46)

Emphasis mine. If they were thought to be damned, no prayer could help. If they were thought to be saved, no prayer would be necessary.
2 Machabees is the most explicit as far as describing a practice with its theological implication, but there are New Testament passages which also have implications of Purgatory.

And whosoever shall speak a word against the Son of man, it shall be forgiven him: but he that shall speak against the Holy Ghost, it shall not be forgiven him, neither in this world, nor in the world to come. (Matthew 12:32; emphasis mine).

The &quot;in the world to come&quot; was interpreted by both Pope St. Gregory the Great and St. Augustine as referring to the possibility of some sins being remitted after death, hence a middle state of Purgatory.
Similarly, in 1 Corinthians:

According to the grace of God that is given to me, as a wise architect, I have laid the foundation; and another buildeth thereon. But let every man take heed how he buildeth thereupon. For other foundation no man can lay, but that which is laid; which is Christ Jesus. Now if any man build upon this foundation, gold, silver, precious stones, wood, hay, stubble: Every man's work shall be manifest; for the day of the Lord shall declare it, because it shall be revealed in fire; and the fire shall try every man's work, of what sort it is. If any man's work abide, which he hath built thereupon, he shall receive a reward. If any man's work burn, he shall suffer loss; but he himself shall be saved, yet so as by fire. (1 Corinthians 3:10-15)

Here there is a distinction between the man whose works abide (who shall receive a reward) and the man whose works burn (who shall be saved &quot;by fire&quot;). The latter case is understood as referring to purgation of the effects of their sins.

Be at agreement with thy adversary betimes, whilst thou art in the way with him: lest perhaps the adversary deliver thee to the judge, and the judge deliver thee to the officer, and thou be cast into prison. Amen I say to thee, thou shalt not go out from thence till thou repay the last farthing. (Matthew 5:25-26)

&quot;repay the last farthing&quot; was understood as referring to smaller offenses and the context suggests a time-limited rather than eternal penalty.