I understand the concept, and that purgatory is not something that is no much taught in Scripture as it is formulated out of a presumed necessity, that being that believers must attain to a greater holiness to enter heaven, than what they had on earth as they overall followed Christ, as is characteristic of true believers, (Jn. 10:27) but therein is the fundamental error.
The Bible teaches that God justifies the UnGodly by faith being counted for righteousness. (Rm. 4:5) While this must be faith of the kind that effects obedience toward its object, including repentance when convicted of not doing so, and Rome does allow for baptism by desire, yet it is on the basis of this imputed justification that one is "accepted in the Beloved," (Eph. 2:1) and has his life in heaven, from hence also they “look for the Saviour, the Lord Jesus Christ: Who shall change our vile body, that it may be fashioned like unto his glorious body, according to the working whereby he is able even to subdue all things unto himself. . (Phil. 3:20,21)
While no man shall see God without holiness, and justifying faith must have that as a fruit, and believers are judged upon their works as they evidence faith and justify one as a being a true believer (faith without such works being dead), yet it is not on the basis of one's own holiness that one either gain acceptance with God, and are already seated together in heavenly places, (Eph. 2:6) being risen with Christ, (Col. 3:1) or enters into glory, but on Christ's expense and righteousness, procured through faith, not in one's merit, but the mercy and faithfulness of God in Christ who thereby justifies sinners by faith.
If one thus dies having that faith, then he/she will enter the realization of their faith, i.e, their faith will be made sight, and thus every mention of the elect after death shows them to be with the Lord, with no distinction being made. The Corinthians were commanded to examine themselves, whether they be “in the faith,” (2Cor. 13:5) but those who were believers would all have been raptured if that occurred at that time, and hence would “forever be with the Lord.” (1Thes. 4:17) Whatever suffering takes place at the judgment seat of Christ, and i believe there will be tears, is not that of purifying one to make them acceptable to heaven. We either die in faith, which will result in being made like Christ when He appears, (1Jn. 3:2) or we do not, and God will despise our image. (Mt. 7:23; cf. Ps. 73:20)
If one achieved eternal life on the basis of his own holiness then the Christian faith would merely be as under the Law, but with a perfect atonement. Under the law, one was accepted with God based upon his performance, with perfection being required, (Gal. 3:10) and thus it was they who would need Purgatory, if there was to be any hope for such to enter glory, but no mention is made of such. Instead, it is taught that the intent of the law was to show man the impossibility of achieving acceptance with God and heaven based upon his moral merit, and thus they needed to look to God for mercy, that ultimately being Christ, by which sinners are declared righteous by faith in the mercy of God in Christ, who became sin for us, (2Cor. 5:21) with a kind of faith that will work obedience being counted for righteousness. (Rm. 2-8)
While Rome sees imputed righteousness as referring to an inner holiness, an infusion, effected by the indwelling of the Holy Spirit, yet the fact is that sinners are made accepted in Christ by faith, and thus would be with the Lord if they died that day. Or whenever, if they have the kind of faith that seeks to be practically what they are positionally.
As for your proof texts that souls must undergo purification after death to achieve the holiness necessary to enter heaven. Your 1st text states: “If any man's work shall be burned, he shall suffer loss: but he himself shall be saved; yet so as by fire,” ( 1Cor. 3:15:), but contextually it has nothing to do with expiation being made for sin and or being purified, but the fire is about loss of rewards for building the church with bad material, not stones like Peter. The fire burns up the fake stones, and the builder loses rewards. Thus Paul says to the Thessalonians, "For what is our hope, or joy, or crown of rejoicing? Are not even ye in the presence of our Lord Jesus Christ at his coming? " (1 Thessalonians 2:19) And to the Corinthians, “we are your rejoicing, even as ye also are ours in the day of the Lord Jesus.” 2Cor. 1:14) And to the Philippians, that being “my joy and crown, so stand fast in the Lord, my dearly beloved.” (Phil. 4:1)
As for 1Pt. 1:7: “That the trial of your faith, being much more precious than of gold that perisheth, though it be tried with fire, might be found unto praise and honour and glory at the appearing of Jesus Christ,” this once again refers to quality of faith, and this refinement of faith to this life, and — as seen in the light of other texts such as 1Cor. 4:5 — to the degree of praise, honour and glory, and not to a postmortem expiation of sin and purification so they can see the Lord.
I could make a better case for purgatory if i wanted to, and resorting to trying to extrapolate Roman Catholic purgatory out of your verses is an argument against it.
Rom 3:22 Even the righteousness of God [which is] by faith of Jesus Christ unto all and upon all them that believe: for there is no difference:
Phl 3:9 And be found in him, not having mine own righteousness, which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith:
I am not expecting you to try to reconcile the teachings of the Church with your own little reality and, frankly, I don't even care to compare and contrast our beliefs. My participation on these threads is only to ensure that the teachings of the Church are not misrepresented, distorted or lied about (which keeps me pretty busy).