“In other words, every man builds upon the foundation provided by Christ. Every man “builds”, his own “building” that is himself (again verse 9).”
No. That is blatantly NOT what Paul is saying. At no time does he suggest the builder is building himself.
“In other words, we are both the building and the builder (of our own lives.”
Not in 1 Cor 3 (in the JB Phillips translation, to aid easy reading of paragraphs):
1-4 I, my brothers, was unable to talk to you as spiritual men: I had to talk to you as unspiritual, as yet babies in the Christian life, And my practice had been to feed you, as it were, with ‘milk’ and not with ‘meat’. You were unable to digest ‘meat’ in those days, and I don’t believe you can do it now. For you are still unspiritual; all the time that there is jealousy and squabbling among you you show that you are - you are living just like men of the world. While one of you says, ‘I am one of Paul’s converts’ and another says, ‘I am one of Apollos’”, are you not plainly unspiritual?
5-8 After all, who is Paul? Who is Apollos? No more than servants through whom you came to believe as the Lord gave each man his opportunity. I may have done the planting and Apollos the watering, but it was God who made the seed grow! The planter and the waterer are nothing compared with him who gives life to the seed. Planter and waterer are alike insignificant, though each shall be rewarded according to his particular work.
9 In this work, we work with God, and that means that you are a field under God’s cultivation, or, if you like, a house being built to his plan.
10-15 I, like an architect who knows his job, by the grace God has given me, lay the foundation; someone else builds upon it. I only say this, let the builder be careful how he builds! The foundation is laid already, and no one can lay another, for it is Jesus Christ himself. But any man who builds on the foundation using as his material gold, silver, precious stones, wood, hay or stubble, must know that each man’s work will one day be shown for what it is. The day will show it plainly enough, for the day will arise in a blaze of fire, and that fire will prove the nature of each man’s work. If the work that the man has built upon the foundation will stand this test, he will be rewarded. But if a man’s work be destroyed under the test, he loses it all. He personally will be safe, though rather like a man rescued from a fire.
Nothing in the text supports that the builder is building his own life, and that God will burn out impurities from that life by pain after death.
Again another astounding claim! From your own translation you just posted (which is a nice one by the way at least for this passage)...
"9 In this work, we work with God, and that means that you are a field under God's cultivation, or, if you like, a house being built to his plan."
Know ye not that ye are the temple of God, and that the Spirit of God dwelleth in you? If any man defile the temple of God, him shall God destroy; for the temple of God is holy, which temple ye are. Let no man deceive himself. If any man among you seemeth to be wise in this world, let him become a fool, that he may be wise.
What? know ye not that your body is the temple of the Holy Ghost which is in you, which ye have of God, and ye are not your own? For ye are bought with a price: therefore glorify God in your body, and in your spirit, which are God's.
beseech you therefore, brethren, by the mercies of God, that ye present your bodies a living sacrifice, holy, acceptable unto God, which is your reasonable service. And be not conformed to this world: but be ye transformed by the renewing of your mind, that ye may prove what is that good, and acceptable, and perfect, will of God.