And when we have free will in that perfect universe we will eventually choose to sin again, and then we will be in a fallen state and round and round we go all over again.
There will be no sin in the new heavens and new earth, because God would have rounded up all evil and destroyed it.
Let's not forget that what caused the Fall of Man in the first place was an evil serpent and the Tree of the Knowledge of Good and Evil.
If Adam and Eve had not eaten of that fruit, there would have been no Evil. Adam and Eve were incapable of doing evil (and thus, sinning) until they were infused with the knowledge of Good and Evil from eating that fruit. (and of course in so doing, they disobeyed God).
In fact, Satan had to trick Eve by making her believe that God didn't say what He said, and that God lied about them dying if they ate it. Otherwise, she wouldn't have eaten the fruit in the first place.
Now, in the New Heavens, and in the New Earth, there will be no Satan, there will be no Fruit of the Knowledge of Good and Evil, therefore there will be no evil. He rounds up all of the Evil, along with its source (Satan) and throws it all in the lake of fire where it will never escape.
It will be impossible for us to have free will and yet never choose sin because if we have the ability to choose it then it is possible, and any event that is possible has a nonzero chance to occur, and any event with a nonzero chance of occurring MUST eventually occur, given eternity. You cannot go citing math saying that the random assembly of a protein is virtually zero and then deny that very same math here.
You can't choose to do evil if you don't even know evil exists or is even possible.
If God defies logic and math, which I fully grant to you as possible or even probable if God actually exists (as a nihilist I reject the notion of our invented mathematical axioms as being absolutely true in all possible realities), then you can say that we will have free will and yet will never choose to sin. But then the obvious question is, "Why didn't God just make us that way to begin with?"
Like everything else,
God created math. Since God created it, He knows exactly how it works, and I'm quite sure that if He ever needed to, He very well could defy it (or simply remove it from existence, or change it). Now obviously if He did that, there would be huge changes happening in the physical world, but eh. That's a whole 'nuther can of worms.
In fact, the very.. uh.. 'characteristic'... of God, "Infinity", is something math has trouble dealing with sometimes. It's an abstract concept that is alien to a finite world such as ours.
Every theology has severe problems when it comes to this issue.
No problems at all, to be honest.