...until he receives common grace from the Father in His call by understanding the Gospel message, inbreathing it, and then man may choose in free will whether or not to believe in Him and accept Christ with faith.
So your reformed friends have been making some progress in at least you see that the natural man hates God, so a change has to take place first. I am intrigued, though by this new hypothesis that the Paraclete breathes in this "understanding" but not enough understanding where the person "chooses" positively for Christ - in other words, there is a chance that not enough understanding was breathed in and the person could still rebel against the command to repent.
It sounds real lame. If you really had understanding that you were worthless scum deserving eternal torment, that there was absolutely nothing to love about you, and that every breath you drew was offensive to a Holy God, but yet "choosing Christ" would mitigate this animosity and you would be released from sin, Hell and bondage and spend eternity in a love relationship with the Creator of all things - now why would anyone choose eternal damnation? Yet, you are saying that the overwhelming majority of people, once enlightened prefer utter eternal destruction. How exactly is that rational or evidence of understanding? To me, it looks like in light of all this alleged understanding, a refusal to "choose Christ" would seem like prima facie evidence of a will still bound to sin and death.
You also introduced a new element called "Common Grace". The presbyterians invented that term a century or so ago, and applied it to explaining why man isn't as wicked in his works as he could possibly be.
Let me say I hate the concept of "common grace" because first, it is an oxymoron in that grace means "unmerited favor", and if everyone receives "favor" then "favor" sort of loses its defining characteristic since there is no one who doesn't receive favor, the favor is gone and it becomes a standard entitlement.
Second, the very idea that there is a non-salvific form of grace is disturbing because a grace that does not save is not worth anything, and does nothing to further the Kingdom of God. Let's say we adopted the presbyterian form of "common grace" that talks about material provision that bothe the regenerate and the reprobate enjoy. Consider Christ's words record in Matthew 16:26 "For whatr profit is to a man if he gains the whole world and loses his own soul?"
But let me take the time to directly attack your hypothesis that the spirit gives man some understanding, but not necessarilly efficacious understanding. I call this hypothesis the Forced Reprobation Policy. In that the person is given exactly one chance to "choose Christ", after that the person is reprobated to Hell forever. There is no reject Christ this Sunday and choose Christ the next. For we have Hebrews 6:4-6 that says that if a person has received this understanding of the holy spirit and rejects it, that it is "impossible for those who were once enlightened...to renew them to repentance." In Christ, there are no second chances.
The Hebrews passage has harmony with Calvinist views towards irresistable grace and perseverance, BTW.
For me, I struggle with a non efficacious grace that is handed out to anyone - it is defective grace, grace without purpose, and if anything, to the reprobate is worse than any grace at all.