So, you are saying God can't allow free will but He can allow evil? Aren't you placing finite choices on God's repertoir? It's not His 'duty"; it's His will.
Free will is a myth; a phantom of our vanity. It's God's world and everything contained therein.
This is good news for those who believe in the Lamb slain from the foundation of the world who know their salvation is due to His perfect sacrifice alone.
I spoke earlier of "free will" being within parameters. Thus, the lost are "free" to sin (from the human POV), and they do. God allows it. It is not His duty to stop it, and neither is it His will to stop it because He doesn't. God maintains FULL control of everything, but He does not zap people causing them to do evil. He leaves them alone, knowing the result will be evil. Since He has no duty to intervene, He is not the cause.
The other way to look at it is that the lost are purely slaves to sin. This does not give an impression of freedom, but is of course Biblical and absolutely true. But even here, God is still not the cause of sin, He allows it in the same way. There is no duty to prevent it, nor a will to prevent it (to the extent He doesn't). God didn't cause the lost to be slaves to sin, Adam did.