The "efficacy" of God's method is deemed unlimited
Efficacy refers to whether or not the desire of God will actually come to pass with regads to the particular case of any given human.
God desires all men to be saved, and gives all men the means to be saved. But some men are not saved, and this is their own fault because they chose not to be among the elect. As to those who are saved, while they certainly willed it, it was God who gave them the will to do so - they can only credit His grace for their salvation, and not themselves. "Without me you can do nothing."
The lists of the elect and damned are closed not because it is impossible for someone to pass from one list to the other, but because nobody would want to.
The atonement was sufficient for all, but efficient only for those who accept it. Christ died for the sins of Judas, but he is still damned because of his perverted will.
That is just a convoluted way of saying: "I chose those who will be saved and those who will be damned." Obviously, if God gives the will to some and withholds that will from others, it is not that some won't but it is that they can't make a decision.
What good is offering salvation to all men if some can't choose to accept it because they were never given the will to do so?
This is like giving half of your children the money to buy candy and saying the other half "refused" to buy it!
If God gives will to some and not to others, then God is to be credited for our salvation as well as our damnation. That is not what the Church teaches.
God offers salvation to all. We choose or refuse His gracious offer based on our free will. It is God who saves us; but it is us who decide if we shall take the train that leads us to God or to hell.
God gave free will to all mankind to use or abuse. We are free to make choices not because we merit it, but by God's permission.
Your view makes for a partial God and the Bible tells us in plain language on numerous occasions that God is impartial.