The Reformed folk that I know might consider that a straw canard...on a string...(though I think there are a couple of posters here that might just agree with that definition). All I know is that every time I try to describe what I see, I have difficulty doing so. On the surface of it, man's freedom seems to be a problem for God's utter rule. The most popular explanation is that God allows for and works with free will. In a sense I guess that's true.
I have recently started calling it autonomous will instead of free will to get rid of some of the confusion around the word free.
I do not see any problem with mankind having autonomous will and God's utter rule.
As ruler, God makes decrees and laws, He also acts as judge and grants rewards or punishments as He sees fit.
The subjects of any ruler have the ability to obey the ruler or rebel against the ruler, even if the ruler is God.
The point is that the life of the believer is one of God's choosing. So the inverse is also true - the unregenerate life is one of man's own choosing. So I see two issues here :
1. To require unregenerate, naturally fallen, dead in sin man to choose God...then to turn around and say that man's choices are wrong and submit them to the God they chose (with the fallen will)!
2. To try and maintain the necessity of an autonomously free will as good and necessary for the same believer who is to submit to God.
Jesus said to seek ye first the kingdom of God and His righteousness.
Everyone that is not a citizen of the kingdom of God will be cast into the lake of fire.
Everyone that is a citizen will be given eternal life.
Man has the choice to petition the King and ask the King to grant him citizenship.
The King can accept the petition or reject it.
If the man has been accepted, then the man still has to abide by the laws of the kingdom.
If a citizen is found to be a lawbreaker, there are many punishments that the King can decree, including exile.
So even before we get to verses about predestination, the problem is very sticky indeed. You have to assume man is at least partly alive spiritually (and somewhat good in terms of eternal matters). Only then can you justify any sort of synergistic explanation of salvation. Take away any of this and it all collapses.
I believe the problem with your scenario is that you assume that being alive is something spiritual instead of something physical.
Paul said we live once and then comes judgment.
That coming judgment is based on our choices in this life.
So since the will that is supposed to be enshrined to validate the salvation of man (as not being a puppet) is deemed not good, what is it we are elevating? Man or God?
God of course.
When a man enters a strange kingdom and requests to become a citizen, he is brought before the king, who makes an examination of the man, and makes the choice of whether to accept the man as his subject or to reject the man's petition.
Whichever decision the king makes, it is the king's decision.
But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:
Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God.
John 1:12-13
When, how and why were they born? They received Him, but where is the will of man?
The man has no power to become a citizen of the kingdom, he only has the power to petition the king.
The power to make the man a citizen of the kingdom belongs to the king alone.