In what you are saying here you are close to the concept that you find in Calvinism and in scripture I believe regarding our salvation. When Calvinist theology says that the cross really did save people they are not saying that nothing else needs to happen - but like you said, there is an inevitable series of things that do happen in the case of the elect. And, since it is an attempt at a complete theological system you have to look at it as such and not logically separate one thing from another. Those he calls he knows, and it is those for whom Christ dies, and the same one's will respond to the gospel and the same ones will be born again and persevere until they finish life on this earth.
Speaking now just as a fellow Christian I can say that this being true does not render inoperative any of the separate things that happen in the life of a person who gets saved. You really do have to decide to be saved, repent and so on. And you will do it by the decision of your rational mind. The fact that in Calvinistic theology it is said that the one who comes to Christ is the one who Christ died for and the one who refuses is one who Christ did not die for is only a reflection of known qualities of God and knowing what God knows. It no way is intended to diminish the importance of passionately calling on everyone to repent, and it in no way means that there are those who might repent and mess everything up so to speak because now you have someone who repented whom Christ did not die for.
If one wishes to only focus upon our role in this, which I whole heartedly agree is to repent and believe the gospel, and be silent and not make any conclusions or comments on God's perspective on such things - I find that totally acceptable and do not think such a person is in any way less complete as a Christian. However; some of the perspectives. even though from God's point of view, like his sovereignty, ability to not only "see" the future, but have it come out as he wishes, are in scripture, and I do object when someone who doesn't want to look into those areas and is not curious about those areas, tries to downplay and pretend that those things are not in scripture and aren't really in effect. People don't have to do theology, and many shouldn't. But that doesn't mean they should come up with goofy, incomplete theology or try to tear apart the work that serious people have done.
But I find error in the statement that Jesus did not make payment for the sins of those who do not believe.
We are described as bought with a price
1 Corinthians 6:20
For ye are bought with a price: therefore glorify God in your body, and in your spirit, which are God's.
1 Corinthians 7:23
Ye are bought with a price; be not ye the servants of men.
The purchase is of blood and not anything else.
1 Peter 1:18-19
Forasmuch as ye know that ye were not redeemed with corruptible things, as silver and gold, from your vain conversation received by tradition from your fathers; But with the precious blood of Christ, as of a lamb without blemish and without spot:
What I find in Scripture is that the unsaved are also bought.
2 Peter 2:1
But there were false prophets also among the people, even as there shall be false teachers among you, who privily shall bring in damnable heresies, even denying the Lord that bought them, and bring upon themselves swift destruction.
Payment for all sin has indeed been made and that makes the offense of refusing the Saviour that much more egregious. If I were to reject a Saviour who is not my Saviour, then I have not rejected anything. I would have never had anything close enough to reject.
It would be like saying I declined the airline in New York to accept free air fare from New York to London while I was in Los Angeles. I was never in a place to refuse it.
How then could someone deny the Lord that bought them if He never bought them?
In my perspective, Calvinism diminishes the work of Christ and says that Jesus did not die for as many people as are sinners.
I contend that it is Scriptural that Jesus Christ has paid for all sin, yet does not impute His righteousness to the unbelieving.
But the righteousness of Christ is not limited to a certain predetermined fatalism. The choice is real.