Calvinism goes beyond this, and says that God makes some people disbelieve. Therefore, it is an excuse for disbelief, and a heresy. God is not the author of confusion. Calvinism is confusion. It has been soundly condemned by all who know and who love the truth. Calvinism denies free will. But your view that regeneration comes first comes from Calvinism. You sound like a semi-Calvinist. Forgive me if I am misperceiving things. Everything I read about Calvinism is that the idea of regeneration preceding faith comes only from Calvinism. No other kind of Christianity preaches that.
The question is: Does the Scripture teach a man must be born again to believe; or does it teach that a man must believe to be born again? You sound like you believe the later, because you admit all people "have the free-will to believe, to seek, to knock and to ask. No one who asks will be denied." Exactly! Calvin and Luther taught otherwise. They taught theological determinism, that free will is not Biblical.
Go figure. PS The opposite error from Calvinism is Pelagianism. The Bible teaches neither. God's grace must come first, but He shows His grace to all, so anyone can believe.
He doesn't withhold His mercy; people withhold their belief. Not everyone believes, but everyone is a potential believer.
We cannot save ourselves. Salvation depends on God's sovereign grace. So Pelagianism is false too.