“However, the Old Covenant couldn’t save.”
And it didn’t have to, since the promise of God to Abraham was quite sufficient, which is the same covenant promise that predicates Christianity. But this promise was not made to unbelievers, but to believers only. There is no such thing as “unconscious” faith, and Christ was not kidding when he said “ for salvation is of the Jews” (John 4:22).
“One can have a knowledge of one’s inadequacy and a need for God’s righteousness to save one.”
And yet no one can have knowledge of one’s inadequacy and need for God’s righteousness outside of the Holy Spirit, and no one has the Holy Spirit who does not confess Jesus Christ. And, again, the scriptures I have provided stand against you utterly.
But earlier you said the grace of God came through the Covenant. However, it was not the Covenant that saved; it was the promise. Your words:
"They didn’t need to, they were all beneficiaries of the grace of God through His covenant."
However, saving grace came not through the Old Covenant which was impossible to obey. Saving grace came through believing in a promise which did not contain the name of Jesus.
In the same way, those who believe in the promise might be saved today even though they may not have heard the name of Christ (however, I do believe this is rare). God can reveal Himself through nature or by whatever means He chooses.
David did not have the Holy Spirit?