God drawing a man to him is what we as non-Calvinists pray for. We pray that God will draw the unsaved to him. The fate worse than death is the Calvinist position that God would, despite our prayers and despite our supplications, absolutely and unconditionally refuse to draw that person to him, because he has simply chosen him for eternal damnation from before the foundation of the earth.
The fate worse than death is the eternal damnation of those who never had any hope of salvation because God never wanted them to have that hope.
We cling to 1 Tim 2:4 because it shows our God to be a loving God who would have all men to be saved. We also recognize a sovereign God who cannot and will not allow unforgiven sin into his presence. There is no contradiction there. There is no dimunation of God's sovereignty if God lays down rules for the application of his grace and those who refuse to accept those rules pay the consequences. God has sovereignly given to all men the opportunity to be saved. God has sovereignly stated that he will accept all who come to him on those terms. God knows who they will be and has sovereignly predestined those whom he has foreknown will come to him to be justified, sanctified and glorified.
That is the Gospel. That is the good news. That you can be saved. Any one of you. Jesus is knocking and all you have to do is answer the door. And you CAN. God is not preventing you from answering the door. And God really loves YOU and really wants you to answer it. Yes there is good news. The keys to heaven are within your grasp. Reach out and grab them. And if you refuse, then you have no one but yourself to blame. That is the Good news. That is the Gospel.
For the Calvinist there is no good news. Just news. Either you are one of the lucky chosen or you are one of the unlucky damned and there isn't a damned thing you can do about it.
The more I think about it, the more I've concluded that they have placed a "modern calvinist overlay" on everything, to include arminianism. They see the world through a particular lens and that lens is colored "modern calvinism."
I call it: As Seen Through A Calvinist Lens: ASTACL
One could make the case that we all see the world through our various lenses. But, what is significant is whether or not any individual can address the weaknesses of his/her particular lens/overlay.
We agree on that.
We disagree on where this motivation comes from.
You say man makes the final step toward God. Man opens the door to God. Man invites God in. Man sees the light and agrees with God.
The Calvinist says God first changes the heart of the sinner and then he believes.
Perhaps one day you'll grasp the distinction. Therein lies the world and all God's blessings.