I think part of the problem is that we're never simultaneously talking about the same thing. There is no difference between the two that I can see.
The objection to Calvinism is that God selects people for hell without ever giving them a real, honest, good faith opportunity to choose otherwise.
The denial of a free will and the insistence on total depravity places all of the blame for damnation upon God Himself as sovereign author of all creation.
It is unfit for a just and merciful God to create simply to destroy. If men have a real opportunity to choose good or evil, then they bear the responsiblity for their actions. Thus damnation is just. But if they are hamstrung by design, then there is no justification for punishing them.
If the Calvinist position is simply that punishment or anything is simply God's perogative and it need not follow any principles of responsibilty or rationality, then we will disagree. But I don't think that is your position.
SD
The problem with the "free will" approach is that it relies upon individuals hearing the "message" and making informed decisions. What happens to those who, for whatever the reason, are not afforded the opportunity to make that decision? Or about the hardening of Israel's heart until the fullness of the Gentiles mentioned in Romans 11 is complete?
Is it any more just of an all powerful God not using this power to have every single person hear the message and make an informed decision?
I've noticed most people think of God's sovereignty as an attribute like love or mercy. It is not. It is God's position. God is our Father and is in control just like my father was in control when I was growing up. My father might have been loving, just, and so forth but these are attributes or characteristics.
While I tend to focus on God's sovereigty (which is God's position), God is also love, mercy, grace, just, etc (attributes). I am confident in the fact that those God want saved will be saved despite our failures because God is in control; fairly, justly, and equably according to His divine nature. The rational for why God does what He does is unknown to us.