Uh, what? Failed to harmonize? I'm confused...How does saying that salvation is entirely God's work not harmonize with John 6:45? You say there is a problem, but you've neglected to state what, exactly, you think the problem is. Certainly, being taught of God the truth we find in His word does not contradict the statement of John 6:44 or my own observation from Scripture that God saves us.
"Mystery"? What mystery? And the idea that John 6:44 is "left out" or rendered false by other verses is itself false.
No person God draws to Christ is naturally inclined toward Him and salvation. As Paul wrote in Ephesians 2:1, every lost person is "dead in trespasses and sins." What does he mean? Well, he goes on to explain:
Ephesians 2:2-3
2 in which you formerly walked according to the course of this world, according to the prince of the power of the air, of the spirit that is now working in the sons of disobedience.
3 Among them we too all formerly lived in the lusts of our flesh, indulging the desires of the flesh and of the mind, and were by nature children of wrath, even as the rest.
How does a man who is spiritually dead, and living under bondage to the "prince of the power of the air," the World, and his own flesh have any inclination toward a God who demands he forsake all of these things? Quite obviously, under such conditions, he can have no inclination toward God and never will have without God's intervention. John 6:44, then, is strongly supported by Paul's words, not "left out" as you assert.
Scripture disagrees very flatly with you:
Romans 8:29-30
29 For those whom He foreknew, He also predestined to become conformed to the image of His Son, so that He would be the firstborn among many brethren;
30 and these whom He predestined, He also called; and these whom He called, He also justified; and these whom He justified, He also glorified.
Here Paul highlights very plainly that through God's foreknowledge He predestines His children to salvation, calling, justifying, and ultimately glorifying them, too. As Paul makes clear, this is God's work, not ours.
Before you start arguing against me as though I'm a five-point Calvinist, I should tell you that I am not a Calvinist but a Molinist in my soteriological persuasion.