The answer is in Romans 5, yet you seem to think it is not there. Why is it that you skim through scripture and never get the point God is making?
What do you mean by "it was God himself that so constituted Adam's fallen nature"?
Do you mean that God gave Adam the capacity to break God's commandment and thus fall into corruption? Yes, God gave Adam that capacity. Moreso, Paul informs us in Romans 5 that this corruption of character would pass on to all of Adam's offspring.
George, did Adam sin by his own capacity to break God's commandment or by God making him break the commandment?
Answer: Adam had the capacity and broke the commandment.
George, did God give us the capacity to fix that corruption by our choice to fix it?
Answer: Humans cannot choose to fix what they have no capacity to fix. It's like an infant playing with an electronic toy. They have the capacity to break the toy, but they don't have the capacity to fix the toy. A qualified person needs to fix what the child broke. The fixing of the toy is entirely that of the one who has the capacity to fix the toy, not the infant who broke the toy.
Adam's brokenness is in each of his offspring. In each person there is a need to be repaired and there is only one repairman who can fix the brokenness.
Is God obligated to fix the brokenness? (Remember, Adam broke God's command, but couldn't fix that which has been passed on to all his offspring.)
Answer: No. God is not obligated to fix what Adam broke. If God chooses to fix what is broken, it is purely because God chooses to be gracious.
Is God unfair if he chooses to fix one broken "toy" but not all broken "toys"?
Answer: He is not unfair. Fair equals justice. If God would be fair, then He would justly leave all toys unbroken since they all need repairing and he didn't break the toy. Adam and his offspring broke the toy.
To fix the toy, you need to pay the repairman, but the cost of fixing the toy is too expensive for anyone to pay. Therefore the repairman (God) can either choose to repair the toy for free, which is an act of grace, or not fix the toy.
Why does God fix one toy and not another?
Answer: He is not obligated to fix any toy, but according to His own mysterious council, God chooses to grant mercy to whom he grants mercy and not grant mercy to others. (Romans 9) He fixes the toys he chooses to fix and he never tells us why. You can make up all sorts of speculations. You can say that humans must do this, that or the other thing to get God to fix the toy. Or you can acknowledge that God simply doesn't tell us and since God is the only one with the capacity to fix the toy, we are entirely at his mercy. In other words...we don't control the decisions of the repairman. He controls his own decisions.
George, you have to live with the mystery. It is not yours to know.