Rev 20:13. And the sea gave up the dead which were in it; and death and hell delivered up the dead which were in them: and they were judged every man according to their works.
Well I've never seen heaven or hell described as having a sea. Only the Earth.
I've never seen anything attributed to heaven as containing the dead.
We have scriptures that speak of the unsaved going to hell.
We have scriptures that speak of Hades, with little disclosure as to what or where it is.
We have scriptural declaration that it is appointed unto man, once to die and then the judgment, so all men die.
Perhaps Lazarus, Jesus' friend, could tell us, he's been dead and brought back to life. But Nope the scriptures are silent about where he went.
We also have no indication that there is such a thing as time outside of this natural life. Only events. Eternity requires no time lest some become "clockwatchers" for ever.
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Here are two different sayings from Paul. He tells the Corinthians that He knows that while we live we are absent from the Lord and he told the Colosians that though I am absent from you in body, that I am present with you in spirit. The first speaks about our relationship with the Lord, the second our relationship with others.
2 Cor 5:6-8. Therefore we are always confident,
knowing that,
whilst we are at home in the body, we are absent from the Lord: (For we walk by faith, not by sight

We are confident, I say, and willing rather to be absent from the body, and to be present with the Lord. [one can safely conclude then that Paul certainly believed that to be absent from this body (flesh) is to be present with the Lord (in spirit).]
Col 2:5. I may be absent in body, but in spirit I am there among you, delighted to find how wellordered you are and to see how firm your faith in Christ is. [Here, Paul is telling the Colossians that he they are constantly present with Him in spirit, and that they should think of him as present with them.]
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I have also not found anything in scripture that speaks of "a cleansing place" between death from this natural life and entry into the presence of the Lord.
It is the Blood of the Sacrificial Lamb of God, Jesus, that cleanses us from ALL unrighteousness. It is by our faith in Jesus that we are so washed in that Blood. Our Faith MUST occur while we are living this natural life. Therefore, if you wish to think of this life, and life within the Body of Christ (the church) as Purgatory, feel free to do so, because what you describe aptly fits the purpose of the Body of Christ.