I think that this understanding is completely antithetical to what Paul actually says in Romans 3. It completely breaks his entire argument down. Paul says that all, both Jew and Greek, are under sin, that there is no one righteous, no not one, all have turned aside and have become worthless, no one does good, and in vs 20 that by works of the law no human being will be justified in God’s sight.
In this passage, Paul flatly denies that there is a faithful remnant in each generation. The only righteousness there is, is through faith in Christ.
Your understanding is also further contradicted by Paul’s reiteration of the problem of sin in Chapter 5. Paul says that we were enemies of God that were reconciled to God by the death of his son. He says that sin and death came into the world through one man and spread to all men because all sinned. It is only through Christ that we are justified.
Paul’s epistle to the Romans was written to both Jew and Gentile. He says this in his introduction in Chapter 1. He says that the gospel is the power of salvation to everyone, Jew and Greek. He then says that the gospel is the righteousness of God revealed from faith into faith (my translation of the Greek ek pistews eis pistiv). This is Paul’s thesis statement. Probably the most meaningful dynamic translation I have seen that takes into account this rather odd Greek phrase is this: For in it the righteousness of God is being revealed beginning and ending in faith. This translation seems to be born out by the content of Romans as a whole. So your understanding is still at odds with that.
Thanks for the dialogue. Regards.