But those who are drawn by GOD are given to Christ. It's those who are NOT drawn by God but are attracted to Christ, nonetheless, for various carnal reasons (such as all those false disciples in John 6) who will fall away, for they were never given to the Son. I see the drawing of God as his enabling power which is efficacious (Jn 6:65).
It's seems quite clear from scripture that this "coming to Jesus" is a process that is expressed in various ways: New birth from above, the sanctifying work of the Holy Spirit and this drawing that God himself does.
What exactly are you looking for here? It seems you want men to have some credit for salvation? Can not both these things be true and a bit beyond what we can understand and explain? The more I watch, read, and engage in this debate the more I see how much we talk past each other and don't try at all to find common ground.
An example of this I'm going to use an example of someone that God brings to a church, the person hears the gospel in truth, God brings them to repentance then and there, they respond to the alter call, repeat the prayer, and God truly saves them then and there. This person is saved and believes exactly as you do, and are 1000% right. For the next guy, he was younger and felt "attracted to Jesus" after seeing his first son born and starts going to church now and then with his wife. He too feels the pull at the alter call and goes up front and does the whole thing too. Then gets baptized as well after. He is told he's saved, thinks he loves Jesus and goes about his life as a "Christian" until tragedy hits. His body is broken in a irreversible way and he is crushed by it. Time goes on and he wants and thinks about nothing but suicide and wanting to die every day uncontrollably.
He loses all hope and thinking he was a Christian feels abandoned by God and reaches the conclusion that there can't be a God for real. Not "mad at Him", but no longer had any kind of hope. This man finds everything on his shoulders too heavy and one day while all along, he finally buckles. He hit's his knees in complete defeat and see's very clearly what his whole life to that point amounted in, him on the ground with no hope crying and broken with no way to fix any of it, and he just "quits". That was what "his way" had earned him and he just quits the whole world.
He wakes up the next day a new creature. He had no clue what happen to him, and it doesn't even hit him until lunch the next day at work, but he after 2 full years of uncontrollable suicidal thoughts at least every 5 minutes of every day he realized, "I haven't thought about killing myself all day!!!" In that moment he knows 2 things, 1. What ever this was, it was from God. 2. Jesus is His Son.
Thinking back on this the man see's no way to say he choose this, now looking back he sees how "quitting" he was turning from "his way", he was making a choice, but there is nothing he can testify but God saved him. When he made "the choice" he was not saved, but when he had no clue what was even going on, God saved him.
So the first guy says "of course our choice is necessary", and the other man says "it was 100% God that saved me", and they're both 100% right, but will both sit on CC arguing with each other all day long making themselves look crazy and disgracing Jesus name.
Do you really not think there's any room in what we don't know about the mind of God and His ways where His complete and total sovereignty over every molecule in creation, works with men's choices to bring about His will for His glory? I personally think this is one of the greatest mysteries of God, but I don't question His sovereignty because I can't understand how all this works. Is there no way in your mind to understand a different perspective and give grace to those who may not think of it exactly the way you do?
These are the questions I've been asking myself lately, and I think so.