Does Calvinism recognize that it has God working at cross purposes to His stated desire?

My favorite personal conceptualization:

1. God gives us free will. Although it's too weak to fully effect faith in Christ, God still foresees this little movement. In this way, all who are serious enough to believe Christ (cf. Mark 9:24: "I believe, help my unbelief") will become the elect.
2. God then moves back in time, makes me one of the elect, and gives me all the irresistible graces to come to faith as well as to persevere to the end.
3. Since my free will is too weak, I need an infusion of God's grace for everything good I do (including choosing Christ). So for this little "work" (if Calvinist wants to label mere choosing "work") I have no basis to boast, and can instead admit (almost) Total Depravity.
4. Please note that this view still give room for God to elect people who don't even have this "little movement" (100% Total Depravity).

Therefore, God doesn't have to work at cross purposes with His desire.

Admittedly, this view is not full 5 point Calvinism because:

• the 'U' is replaced with a 'C' (Conditional Election Based upon God’s Foreknowledge)
• the 'T' is not full total depravity either, to allow for that little desire for faith. I imagine this is like someone with a New Year's resolution to lose weight but needs God's grace to keep it.

I found a 2013 paper God's Will & Man's Will: Predestination, Election & Free Will, but this view is not among the five described. Maybe it should be called the Catholic view which is based on Catholic interpretation of St. Augustine.

I'll leave this answer to be deleted by a moderator if it is deemed not Calvinist enough :-).

In my experience, though it would be difficult to quantify the matter, most 'Calvinists' would repair to the Authorised Version (KJV) to respond to this question, therefore :

The Lord is not slack concerning his promise, as some men count slackness; but is longsuffering to us-ward, not willing that any should perish, but that all should come to repentance. [2 Peter 3:9 TR/KJV]

The TR, Textus Receptus, has εις ημας (toward us), ἡμᾶς being the plural of the first person (us).

The Westcott & Hort/Nestle Aland text has εἰς ὑμᾶς, see Biblehub and this is rendered 'toward you', ὑμᾶς being the second person plural.

This, as many of the differences are between these two Greek texts, is a subtle difference.

For Peter to say 'us' means himself and that small body of persons whom he addresses, the saints - believers.

For Peter to say 'you' widens the context to (possibly) any group of persons he might address at any time : it is indiscriminate.

Which is exactly the point of the doctrine.

God's gospel is preached to all nations, Matthew 28:19,20. The literal Greek conveys the 'discipling of the nations'. Out of those nations, some will believe. These are to be baptised. Then - and only then - are they to be taught to observe all things that Jesus commanded.

It is clear that Peter addresses his second epistle to 'them that have received like precious faith with us', 2 Peter 1:1, that is to say , those who have , out of the nations, shown 'obedience to the faith' Romans 1:5.

Of these, and of these alone, Peter says :

[God is]... not willing that any should perish, but that all should come to repentance. [TR/KJV]

Paul the apostle preached and taught election and predestination.

So did Jesus himself.

They were not invented by John Calvin.

Whether election matters or not is clear by its frequency in scripture : over 25 times (election and elect) mentioned across twelve different books in the New Testament writings. Jesus speaks of it, reported by three different authors, Paul speaks of it in six different epistles, Peter speaks of it in both his epistles. John also mentions it.

The doctrine of Christ is known by the preaching of those who are sent of Christ to preach it and is known by those who experience salvation under that preaching.

The divide and the argument that prevails over this issue (Calvinism/Arminianism) is resolved by being obedient to the Apostles (and not changing the text of what they uttered) by hearkening to the preaching of genuinely called Ministers of the Gospel, and by humbly receiving the truth and receiving the concomitant ministrations of the Holy Spirit which accompany the Word of God.

In thy light - shall we see light, Psalm 36:9.

If the light that is in us be darkness - how great is that darkness, Matthew 6:23 and Luke 11:35.