What if they are both true and not exclusive? What if some are just supernaturally chosen. Like it or not, Scripture clearly seems to indicate that some are. But, what if everyone else is truly called--the opportunity is truly available for them to come to God through Jesus of their own free will?
Let's be honest: If you think that people are truly chosen and predestined, then whether you and I are obedient to preach the Gospel or not won't affect the chosen from being chosen and coming alive to God. If it does, you have just sacrificed some of that sovereignty that you think God is giving up because He allows free will. It would mean that because a chosen one isn't obedient, other chosen ones wouldn't come to God. That means that a human's actions would have prevented God's chosen ones from coming to Him.
So, why preach the Gospel if the chosen will be chosen regardless and the unchosen can't answer the call? It is only Good News to the chosen ones--who don't need to hear you preach it anyway because it is going to happen regardless OR is it called Good News, because anyone can answer the call who isn't chosen?
It is poor logic that reasons, "because something God has determined is set in stone, therefore I have no responsibility in the matter". The first most obvious reason the logic is bad is because when anything happens, it was caused, and all day we see how (at least in part) most things happen --they are caused by something else. Although we usually would not call these causes supernatural. God uses means to accomplish his ends.
Yes, he will cause me to stumble on a post hole while my arms are otherwise occupied and I fall in a most undignified fashion, for the watching pleasure of those who patiently await my relevant comment for the moment. But somebody dug that hole! Did he have to wait for the hole to be dug by chance to think of causing me to stumble on it, so that my companions would have a humorous account to relate at my expense upon our return? Of course not. He caused the hole to be dug. But somebody dug the hole.
For a believer, perhaps the second most obvious thought, is that regardless of the vagrancies of human reasoning, God's commands remain his commands. He told us to preach the gospel, and so we must.
Another runs close on the heels of the second, contradicting the notion you pose --that it is possible for a person to make an absolutely free choice for or against Christ. And like it, you sound like the one who is chosen by God, has not choice but is (apparently) forced into his saved condition. Neither are true. Those that are not chosen for God's own indeed are not interested in coming to him on God's terms. There is only one truly sovereign, and all others are influenced exactly as God planned. The chosen don't become saved by their own choice, but by the work of God in them. God indwelling a person is their regeneration, hence their changed mind indeed will choose God. This is a most gentle operation, yet never fails to happen. The heart may be even very slowly convinced, and that, by the preaching of the Gospel, among other things.
The spirit of a sinner is in wholehearted agreement and cooperation with their sin. But yes, they are constantly impelled one way or the other by causes. Though they do indeed choose, their choice is always bound by their sinful nature.
You jump a huge logical gap when you equate "called" with free will. I will assume you did so for simplicity just to make your point. But I have to think, when you contrast free will with predestination (something the Bible does not do, unless "free will" means sovereignty), your use of it means sovereignty. Well, sir, there can be only one absolute sovereign. And absolute in that regard logically demands not only that nothing has any rule over him, but also that all things are subject to and in control of that sovereign.