It seems to me that the very first part of your paraphrase ("If you do this...") necessarily implies that man has to will it before God will do it. That, as I read it, is contrary to what John is saying. Neither the fleshly will nor the will of man at all is bringing this about. It is "of God". If the will of man is required to validate and approve of God's will (which seems to me the way this text has to be read to line up with the way you are reading it), then only the doing can be said to be of God - and not the willing. That is partly negated by that verse itself, but we also find that it is only God who wills AND does of His good pleasure :
Wherefore, my beloved, as ye have always obeyed, not as in my presence only, but now much more in my absence, work out your own salvation with fear and trembling.
For it is God which worketh in you both to will and to do of his good pleasure.
Philippians 2:12-13
And Proverbs tells us (as does the Psalms, I think) that man may make plans and will to do things, but ultimately it is God who dispositions events. So if you are asserting that God has said "Come" (and maybe even "Do") and He is waiting for those who do so to do so of their own volition, you have a situation where the unregenerate, reprobate sinner whose heart is wicked and deceitful above all things has to be relied upon to do what he doesn't naturally will (but do so of his own free will). And, when he does, then (and only then) can he be born of God (but it is not of his will at that point since he's already surrendered it). Because John 1:13 is clear that the willing (and the doing) is of God. But if God can't do His will until we come to Him of our own will, then the whole thing hangs - not on God's will, but ours (in our natural, fallen, deceived, wicked state).
It seems to me, then, that the salvation of man has to hinge on one of two things - God's will and ability or man's will to overcome his nature. Man's will to do so can only come if God changes man (or if he is naturally good in inclination). And at the very least that requires the truth be laid out in full view of the sinner - such conviction only comes from God. And conviction requires the bypass and/or penetration of a heart inclined to sin (and even ignore conscience). And, again, I'm brought back to John 1:13. If the willing to be saved is of the man himself (separate from the will of God), then God has to sit there and rely on the will of sinful, reprobate man to choose Him. Without a change, it can't and won't. So I can't help but apply that passage to the whole of salvation.
Is man's "free will" diminished any? From a human perspective, it certainly is not. But if the depths of depravity are as great as Jeremiah 17:9 says (and I believe they are), then just to get to a point of saying "Yes" to God (I speak from a human perspective here), God has to do something else first. He doesn't save us just so we can escape the consequences of sin, but He does it to make us new. And we don't even will that (according to John 1:11-13).
