In human's free will is defined as the capacity to make choices within our capacities as humans. We can lie, we can act contrary to our instincts. God doesn't have "instincts" in this manner. Is not human in his manner, doesn't have human choices to exercise free will in this manner.
So my mistake was in trying to follow your premises of God and free will.
Let’s see if I can once again muddle things up:
God has will.
Natural man has the will to sin or not sin.
Saved man has the will to sin, not sin, or do good works.
Natural man does not have the will to choose God.
Natural man does not have the ability to obey God.
Natural man is dead to God, and must be resurrected by God in order to have faith.
Once that happens, natural man has been transformed into saved man.