I have to agree: excellent question and very thought-provoking.
For me, the most important answer is to be found in Genesis 1:26 -- that man was created in God's image and likeness.
Does God have free will? Of course He does. So do His children.
Genesis 2:7 shows man being created again -- a second time, but this time from the dust of the ground. God's image and likeness is not dust (chemicals). This second "man" is not so free, but more deterministic -- a cog in the machine of physical reality.
The combination of this Genesis 1:26 "man" and the Genesis 2:7 "man" is reinforced by Genesis 6:3 where it somewhat cryptically tells us that man is "also" flesh. If he is "also" flesh, then he is something else, too. That something else was created in the image and likeness of God. And the Heavenly Father will not always strive with the flesh, because once his children are saved, there is no longer any need to dwell on or near Earth.
We have free will, because we are creators like the Heavenly Father. This is why Jesus would tell us that we can do the things he did and even greater. This is why Jesus repeatedly said that it was the victim's faith that healed them and nothing that he had done for them. And this is why Peter could walk on water, if only for a moment, before doubt set in.
Now, when I say that "we are creators," I am talking of the true self (Holy Ghost, immortal soul, spirit), within. Too many confuse this with ego, the selfish and separate false self which is the blindfold on our spiritual eyes.
When Jesus said that salvation was for the sinner and not the righteous, he was revealing a wonderful truth -- that only through humility can we claim salvation. We have to forgo ego in order to find true righteousness. Those who think they have it made will discover that they have been left behind. Such are the wages of the lazy and arrogant.
You can only discover true free will by replacing ego with humility and by assuming perfect confidence, unconditional love and 100% responsibility.