There is no better way to see what the message of salvation was than to consult the men that first preached it. For example, Paul, in Romans 10, says:
9...if you confess with your mouth that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved. 10 For with the heart one believes and is justified, and with the mouth one confesses and is saved (Romans 10:9-10)
This scripture (and others) plainly say that you are saved because you believe. The sentence begins with IF which introduces a conditional sentence in which the result, salvation, isdependent on the hearer's response which is faith. If anyone acts upon the condition the result (salvation) will most certainly follow or else the promise is false.
All the calls to salvation I am aware of are framed in more or less the same way. No scripture says, "search your heart to see if you feel the marks of grace. If you do then you are saved already. God does not want our faith to rest on the shifting sands of our emotions but on the sure promise of His Word. Acting on the truth is what saves a person.
Now you might say "no one comes to the Father unless the Spirit draws them" and, while this is certainly true, just because the Spirit is drawing a person does not necessarily mean they will yield. There are many instances of people being strongly influenced by the Spirit to believe and surrender but they refuse. Of course, if they resist the Spirit in this manner then they end up with a hard heart which is a perilous state to be in. Nevertheless, the Bible teaches us that the Spirit, omnipotent though He is, can be resisted, quenched, and grieved by puny human beings(Acts 7:51, 1 Thessalonians 5:19, Ephesians 4:30) This is possible only because He has not chosen to overpower our wills. That is more characteristic of demons who take possession of humans like dolls, speaking out of their mouths and tossing them about without their consent. The Holy Spirit does not do this.
All you're doing is taking rigid interpretation and applying it to God.
God does not justify evil, and so He will not draw those who will reject Him. Fate is simply the reality of an omniscient and immutable god, it is something seen all the way back to St. Augustine in the 4th Century.