Man does not set the terms of agreement with God. Man, according to his nature, will never choose God because God demands that they die and be made a new creation in Christ. As long as a human thinks s/he can set the terms of agreement, they will never be saved.Rom 10:9; if you confess
Joh 3:18; He who believes
Joh 5:40; you are unwilling
Eph 1:13; having also believed
Rom 10:13; WHOEVER WILL CALL
Joh 7:17; If anyone is willing to do His will
Man is responsible for the free will choices that they make, and as you can see from the verses above they can and some do choose to follow Christ Jesus.
Martin you do seem to have a problem with logic in your post. You want man to be freely drawn irresistibly. If it is by an irresistible force that one is drawn then man does not have a choice thus it is not done freely.
Salvation isn't an issue of human willpower. It's an issue of God's supremacy. Either God saves you or you are unsaved. That's the terms.