You said it....'what he CHOSE to do," not what God determined for him to do through secondary means etc... That is the difference.
Do not confuse the state of Adam in Eden with the state of fallen Adam.
Adam in Eden had full understanding and complete freedom of choice. Neither existed after the fall. God did not "determine" Adam to fall, but it was the freedom of choice that Adam chose Eve over God.
Agreed, if left alone no one would come to repentance. But God didn't leave us alone. He sent Christ, the scripture, the gospel, apostles, the church and messengers to make an appeal to every creature to be reconciled to Him. You can't take passages which teach of our inability to call on God and apply them to your presumption that we are born unable to answer when God calls on us.
The very point being made is that it is God who calls and God that makes us able to respond.
Until the time God works, we are made unacceptable and unrepentant by sin just as Adam - unrepentant.
Adam never approached God after he chose Eve over God. It was God that sought Adam.
Throughout the Scriptures it is God that does the choosing, never does man do the choosing. God is always making the claim on man, man does not first make the claim on God. Man is a falling dead creature. Many on the way down may hope, and scheme, and plan, even barter in hope of finding an escape, but eventually all will hit the bottom. All are dead, already.
Adam had such a wonderful chance to look the creator right in the eye, humble himself, accept responsibility and be cleansed. Just as a believer has that ability in Christ.
But Adam didn't because his fallen nature did not allow for that condition. He was trying to cover his own shame by blame and excuse. He had tasted of the heavenly and there was no ability of him to repent.
The condition of all without Christ is the inability to generate "Godly sorrow."
However, that is not the condition of one who is a believer. The believer does have Godly sorrow and does repent. It is a result of faith that God implants and the work of the Holy Spirit given by God to that believer.
God does the choosing, not man.