A fine essay appreciating the practical importance of what might seem purely theoretical limits on scientific inquiry. Gödel reportedly never understood why his theories did not transform the practice of mathematics and logic the way that relativity transformed physics, but perhaps that change is now beginning. Indeed, I think you understate the limits of predictability, focusing on the Lorenz problem of insufficient resolution of initial conditions. In my article, I analyze unpredictability arising from counter-predictive processes and find in them a basis for a limited amount of free will.
The canonical counter-predictive process is from Turing's paper on the halting problem: a program that reads and executes a purportedly perfect predictor of its output, notes the output, and outputs something different. The violation is purely of prediction, quite consistent with the physical world being deterministic, just as there is no problem for determinism when you write 1 = 0, either in the physical act or your neuronal configurations as you write. The process is like a device that displays a green light when you push the red button and a red light when you push the green button. This special sort of unpredictability remains consistent with forward determinism, and I think also with the theory of superdeterminism you've written about.
The history of analysis of counter-predictive devices and the consistency of physical determinism with inability to accurately predict human actions when the prediction is revealed are dealt with in Jen Ismael's article for The Monist, which I cite. My work extends the phenomenon of unpredictability to revealed predictions and a range of human activities such as defiance of commands, laws, claims of fact, and ultimately to the interaction between the conscious and unconscious mind. For example, if there is algorithm and sufficient data to predict whether you will lift your finger, you can run the algorithm yourself, read its prediction, and do the opposite. If you don't do the work, your actions may be deterministic and predictable, but if you do the work then the self-referential thinking about your thoughts creates the possibility of defiance of the prediction. Your choices arise out of your own nature, yet are neither random nor predictable, though they may still appear deterministic from an "outside" perspective--a degree of free choice to the extent self-referential.
I did read your clever article about the free will function and understand that you think scientific determinism eliminates the possibility of anything resembling what we would want free will to be. I didn't cite it because your free will function, while unpredictable, had no "human" motivation and no resemblance to the common human subjective experience of making choices. Also, you had to resort to hiding your transcendental number (akin to a Turing oracle) from the human subject to make it work, which I think is not a legitimate assumption in this context.
That said, I'd very much like to know if and why you think my argument for a somewhat free will are flawed.
Steve Brock