No one cares about your ideas if you ignore the FACT that the Holy Spirit had Paul write that no one seeks God, no not one.
Paul is quoting Psalm 14 which single's out those who say in their hearts that their is no God and who seek the destruction of "the righteous band". It is those who do nothing righteous, no not one. It is they who do not seek God because they claim He doesn't exist.
The Calvinist is accusing Paul of quoting the Bible out of context. That's not what Paul is doing. Those quotes are indexes to passages that Paul's audience already know about. Rather than quote entire chapters, the listener is enjoined to re-read the whole context of the quotes and think about them. Jesus did exactly the same thing in the Gospels.
The Holy Spirit had Paul extract these truths from that psalm. Your attempt to explain it away is defective. I do not agree with your " take" on it right from the start anyhow but you will believe what you want.
I will stick with what the HOLY SPIRIThad Paul communicate.
You didn't stick with Paul's quote of Psalm 5, did you (see Romans 3:13)? What does that Psalm say? It talks about those who have rebelled against God. That would be Israelites. This makes Paul's point in Romans 3 that Jews also are under sin, not only gentiles.
Then in Romans 3:15-18, Paul quotes Isaiah 59:7-8 which talks about how Judah has been separated from God because of their sin, though God's arm is not short that he cannot deliver them. Once again, making the case that the Jews have no advantage over the gentile simply because God gave
them the oracles of God. They too can fall under judgement.
The Calvinist doesn't believe in understanding context. It seems the Calvinist HATES context. The Calvinist takes a Talmudic approach to the Bible, finding support for their views with cut/paste sentences that are separated from their context in order to make the Bible say something that it's not saying.
Calvinist treatment of Romans 3 is proof that that is exactly what they are doing. I don't expect to persuade you, but others who read this may re-think what they have been told and look into Paul's quotes for themselves instead of covering their ears and saying, "La, la, la, la, la....".