I agree with you.
Imagine a wealthy quadriplegic. He has free will. But he can't do anything. So, he gives his free will orders, and others do it.
Or imagine AI that comes to life, in its early stages. It has artificial free will, even though it may not realize it. This is said right in the name Artificial Intelligence.
Cause and effect shows us that we don't have free will. If we have free will, it is in a form that we don't scientifically understand, yet. But the fact that we have such determined artificial free will as we have, suggests that there is free will in us in some strange way.
Think of the implications of us having free will when all we can see is artificial free will. The basic implications of this are twofold (without looking at the God idea):
1. We are all artificial intelligence, or;
2. Either we free-will control C&E through some kind of space/time "hacking" of the basic initial cause(s) of all things, or our fundamental science/understanding-of-physics is completely wrong.
''But the fact that we have such determined artificial free will as we have, suggests that there is free will in us in some strange way.'' Right.. whatever makes you happy bro. If we have the tiniest amount of free will then cause and effect is meaningless, again, it cannot be both, if there is no free will and everything has a cause that has a cause, etc, then it's gods fault.
You assume that our free will has to be located within a part of the universe. We don't know that there isn't a way that our free will is supernatural, and only attaches to the natural in some mysterious way. After all, without the understanding of how something works, the thing might seem to be supernatural. So, why not, if free will IS supernatural, might we not only never find a scientific understanding for it, but also definitely prove that it exists supernaturally, sometime?
We don't know that we can't have it both ways.