Isn't this a strawman? Who says the only alternative to predestination (God chooses who will be saved) is that God wants everyone to be saved but somehow cannot accomplish it?
I would argue this a different way. Your claim is essentially that God does not appear to be saving everyone, therefore (since God can accomplish what He wants) there must be something He wants more than saving everyone. And based on that something, e.g. His will, He chooses who to save.
But my claim is that the something He wants even more than to save everyone is that He wants us to have free-will so that we can choose to be saved or not. Therefore what God wants is still being accomplished.
You are correct that God's saving designs are penultimate and not ultimate. You are incorrect to assume that it is free will that is ultimate. God's glory is: A Passion for Glory
BTW, answer this question: If free will exclusively determines salvation, then will people burn in hell because Johnny (for instance) doesn't get up off his duff and preach the gospel to Fred (for instance)? Fred then dies the next day where God simply tells him: "Oh, well, at least you have your free will. It is a marvelous gift I gave you, isn't it. Enjoy the Lake of Fire."