I agree with you that the OT law did not justify. That OT law required the work of perfect flawless sinlessness to be justified. Just one sin and that would bring the curse of the law upon one Gal 3:10. That OT law showed no mercy, it only condemned.
The OT law requirement of perfect sinless is why Paul would say "
But that no man is justified by the law in the sight of God, it is evident: for, The just shall live by faith." Gal 3:11. Again, no one, other than Christ, kept the OT law perfectly and since no man could keep that OT law perfectly no man could be justified by that OT law.
You speak of the faith of those in Heb 11. In Gal 3:12 "
And the law is not of faith: but, The man that doeth them shall live in them." It does seem strange Paul says the OT law is not of faith after reading about the faith of those OT characters in Heb 11. Again, faith under the OT law did not matter when being justified what mattered was what one did in keeping the whole law perfectly. One commentator puts it "
The Law did not even require faith, as seen in the quotation Paul gave here from Leviticus 18:5, the meaning of which may be paraphrased, "No matter about faith; do the Law and live. This was the essence of Judaism." Coffman.
Romans chapters 1-4 briefly:
Rom 1 Paul proves the Gentiles are sinners
Rom 2 Paul proves the Jews are sinners
(Nowhere does he ever say Jew and Gentile were born sinners)
After proving both Jew and Gentile are sinners Paul says all (Jew and Gentile) are under sin Rom 3:9.
Those under sin are in need of justification. Paul spends about the first 2/3rds of Romans 3 explaining what does NOT justify (OT law) and last 1/3rd about what DOES justify (faith).
After proving Jew and Gentiles are sinners (Rom 1 and 2) Paul addresses the Jews beginning in Rom 3 and the OT law that was given them. Having the OT law was a major advantage the Jews had over the Gentiles. Yet one thing that OT law could not do was totally justify the Jew for it required perfect sinlessness. Was the Jew under the OT perfectly sinless? No! (Rom 3:9) The Jew sinned just as the Gentile. Paul cites from the OT verses that proved the Jew sinned in Rom 3:10-18. Then in Rom 3:19 Paul says "
Now we know that what things soever the law saith, it saith to them who are under the law: that every mouth may be stopped, and all the world may become guilty before God."
It was the Jew who was under the OT law so we know verses 10-18 was being specifically directed at the Jews who were under that OT law. Paul in v19 is essentially telling the Jews that your own law given to you says you are sinners hence no better than Gentiles.
So Jew and Gentile have sinned and are under sin and need of justification. We see from the first part of Rom 3 the OT law could not provide that justification. Then what can justify the Jew and Gentile? Paul tells us in the last part of Rom 3 what can justify "
Therefore we conclude that a man is justified by faith without the deeds of the law."
Paul says "FAITH" justifies. he did NOT say faith only justifies. Faith justifies apart from the strict flawless work of law keeping the OT required.
Rom 4:
Paul gives an example of what he just spoke about in Rom chapters 1-3. Paul picks two men to use as his example, not any men at random but two men the Jews would know about very well Abraham and David. Abraham was a Gentile, David a Jew and Paul said in Rom 1-2 Jew and Gentile have sinned, hence need justification. Rom 3 Paul shows the OT did not jsutify for it required sinless perfection. Were Abraham and David perfectly sinless? No both men sin, were "ungodly" Rom 4:5. So neither could be justified by the OT law. So they would have to be justified by FAITH.
Rom 4:5 "
But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness."
I see Rom 4:5 a restatement of Rom 3. Abraham and David "worketh not", that is, they did not work to keep the OT law perfectly both sinned hence could not be justified by the OT law. "But believeth" that is, both had an obedient faith in doing God's will.
Rom 4:6 "
Even as David also describeth the blessedness of the man, unto whom God imputeth righteousness without works,"
Again, "without works" refers to the strict flawless work of law keeping the OT required to be justified. Both men had obedient works in doing the will of God but neither had perfect sinless flawless works.
Rom 4:7 "
Saying, Blessed are they whose iniquities are forgiven, and whose sins are covered."
Does God forgive and cover the sins of the man who remains disobedient to Him or the man who obeys Him? Those who obey.
Rom 4:8 "
Blessed is the man to whom the Lord will not impute sin."
God reckons sin or righteousness to a man. David was reckoned righteous by his obedient faith (not by faith only).
ROm chapters 1-4 the only work Paul says will not justify is the flawless perfect law keeping the OT required. Nowhere ever did Paul eliminate faithful obedience from being saved. Paul is contrasting perfect flawless work of law keeping versus an obedient faith.