I'm clearly with you on points 1, 2, 3b and 4. Point 3a I would alter a bit. It takes a little explaining.
I believe that because no one naturally wants God and his salvation, he moves to examine and influence the hearts of ALL men, for them to form a decision over time for him. And for many, especially at a younger age, this genuine and 'correct' decision made is not readily noticed as being really a conscious decision. It starts out as a heartfelt bias towards God and his creation first...my wife came to Christ that way during her early years of 8-10 years old. She cannot point to a single day or event where she chose God for salvation.
Now eventhough God influences and interacts in the hearts of ALL people, and supposedly many people have made a choice over time, this does not guarantee salvation for all of them. If and only if a genuine and authentic decision was made authenticated by God, for Christ . This decision could be made our of deception, thinking they said the right things and gave lip service to all scriptures and went to church religiously and prayed a lot, and they even thought they used their own will power over time to really save themselves when that would be utterly impossible.
If over time they continue to deceive themselves, eventhough God attempts to bring them back and win them over during their lifetime, then they are lost and of course God CANNOT choose them fraudulently and without proper justice. God can only go so far to win his love for salvation and not force it upon a person. God wants all to be saved as scripture reads, although it is not possible with especially the real evil folk.
No, God does not play the chance game either. He does not deliberately choose hearts over others by calculating the probability of genuinely choosing him or her in advance like with a 'the survival of the fittest' mentality.