No, you are wrong here. The Law teaches us about sin and through the Law comes accountability - NOT justification.
The law cannot teach us about sin without at the very same time teaching us about righteousness. Don't put words in my mouth which I never said. I never said the law "justifies" sinners and the righteous don't need justification. The Law defines good and evil. God is the one who justifies us (not the law) and He justifies us on the basis of Christ's satisfaction of the law. The law must be satisfied or else God relinquishes the right to be recognized as God.
But God's righteousness is manifested APART from the Law (not through the Law, not based in the Law, and not a matter of moral behavior in accordance with the Law).
Wrong! Romans 3:21 demands the righteousness of God is revealed THROUGH and BY the Law and the prophets but in addition to that, it is revealed APART from the law in the Person of Christ.
But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets;
Not the words above. "but NOW" is the righteousness of God manifest without the law referring to the incarnation (v. 22). However, before the "now" the righteousnes of God was manifest by the law.
Righteousness is God's faithfulness to forgive those who are "in Christ", who are now members of the New Covenant. The mark of righteousness is not moral behavior but faith in God through Christ.
God is faithful to forgive us based on the righteousness and death provided by Christ, which was the covenant obligation of the second Person of the Godhead. The term "righteousness" is a MORAL term especially when connected to "faithfulness" as "faithful" refers to ACTIONS of moral value that are either "righteous" or "unrighteous."
The crux of your view is your failure to understand that a fig tree brings forth figs not walnuts and only a MORAL heart can produce MORAL values of right (righteousness) and wrong (unrighteousness). God's heart is a MORAL heart as "righteousness" is a MORAL value.
Righteousness of heart is not ATTAINED by righteous works (thoughts, words, deeds) but is what produces righteous thoughts, words and deeds. God IS righteous because His heart IS righteous and therefore faithfulness is the product of a righteous heart and is the manifestation of righteous thoughts, words and deeds.
You have a cart before horse mentality when it comes to this subject. Y
ou think that if someone actually does the works of the law that makes them righteous when all it does it demonstrate they are righteous. Christ performed the law in our stead but his performance did not MAKE him righteous nor did it ATTAIN righteousness before God but it DEMONSTRATED he IS righteous and the standard of the law declared it to be such but NEVER OBTAINED IT.