Your straw man is coined Hyper-Calvinism.
Calvinism which is also Luther's understanding (read bondage of the will) Augustine's and apostolic see below:
It is perplexing that physicists acknowledge light to act as both a particle stream and a wave. The mystery they, without hubris of conceit, observe. Yet pelagians cannot be as humble to look at special revelation and subject their understanding to it alone. Calvinism gives the glory of election to God alone.
What you are missing is that that faith, that pouring of the Spirit, that calling to salvation is available to all.
Yes, Jesus said that no man comes to the Father unless the Spirit draws him - and Jesus made clear that that “drawing to the Father” is there for everyone to respond to. “Come unto Me all that are weary and heavy laden, and I’ll give you rest.”
Yes we cannot save ourselves - that is only accomplished through the life, death, burial, and resurrection of our Lord Jesus Christ - but we have to respond. Jesus’s sacrifice is sufficient for the salvation of all mankind. “For God so loved the world” means just that - the whole of humanity.
The Bible is filled with the command “choose this day Whom you will serve”, “follow Me”, “resist the devil”, “come unto Me”. None of these commands make sense if we do not have the ability to respond ourselves to God’s grace.
God giving us the freedom to grasp onto to His lifeline of salvation in no way takes away from His glory or sovereignty. He sovereignly chose to give us the ability and freedom of our wills to accept or reject Him.
If we don’t have that freedom, then how is it loving Him if we choose Him since we were pre-programmed to do so? That makes no sense to me.