We need no help at all to sin, so that is "closer" to the normal human idea of free will choice.
According to Protestant theology, repentance is God-given. That means Adam did not repent because God didn't want him to repent.
Perhaps not immediately, but I thought we both think he repented LATER. I would say he received saving grace later. As I understand your belief, Jesus went and snatched him out of Hades, thus proving that Adam did repent at some point. That was just a timing issue for God's purposes. Once the sin was committed though, the deed was done and could not have been undone, as if it never happened. At that instant, he needed saving, regardless of when he repented (assuming he was saved).
In other words, God is behind Adam's pride. Don't you see, FK, this theology puts the blame on God and not on man?
God is behind God's plan, not Adam's pride. God had His reasons for delaying the inevitable. He does the same with many of His elect, since many are not saved at the instant we reach the age of reason (like me). This is perfectly normal and common.
To repent is a choice. There is no such thing as "natural" human behavior. Everything men does is learned.
As I understand your belief, Jesus went and snatched him out of Hades, thus proving that Adam did repent at some point
I don't see why He would have done that. I don't believe it. That's for sure.
Once the sin was committed though, the deed was done and could not have been undone
The Christian teaching is that by repentance the sins are forgiven, committed to oblivion, which is as good as if they never happened (great is God's mercy).
God is behind God's plan, not Adam's pride
But if God is sovereign and doesn't allow free will then Adam's pride is not his pride but part of God's will and plan. Then why would Adam be punished? For obedience?
Again, I call your attention to the scriptural fact that God called out to Adam, "where are you?". For this to make any sense, the inspired author was telling us that Adam was making his own choices.