" From what I can see the issue is foundational to everything and yet no one has a definitive answer."
I can see that choice is part of your argument and from what I've observed it's a key piece of the puzzle. Let's take a more general viewpoint and not just science. Are choices and the ability to make them really evidence of freewill.
That said one thing worth mentioning is awareness has a big role in freewill. We've all had the experience where we resist our urges which I take as weak evidence for freewill and a requirement for this ability is that we must be aware of the influences that compel us to act in a certain way. If for a moment we let our guards down we're back to behaving like an animal - instinct driven and machine-like.
I generally agree with this, most of the objections you've got stem from an interpretation of the word 'choice' different from yours (you're obviously referring to free choices here, which a deterministic machine isn't able to make).
However as someone mentioned, if people's actions were predetermined then it was also predetermined that what we call science would evolve the way it does, so science "moving forward" does not imply free will, however in order to believe in the absence of free will we have to leave plenty of coincidences unexplained.
That is not true!
For example, defining knowledge as a justified true belief is clearly unsustainable.
Edmund Gettier famously breached the stalemate in 1963 with his counterexample cases. The entanglement phenomenon also decisively breaches the classical JTB definition. The problem is now completely up in the air, even on the empirical side of things.
Furthermore, only empirical knowledge could possibly ever be correspondence-theory "true" and therefore JTB knowledge. Axiomatic fields such as mathematics, which are never correspondence-theory "true", are not knowledge in that approach. So, what are they then?
RA, just a thought, would it make better sense to ask …"Can you do science without a strong sense of wonder"?
In other words, if we were to use logic, one could argue that a 'synthetic a priori' proposition is essential in science for moving the thought forward, as well as realizing the resulting discovery and uncovery of such things... ?
So I suppose the 'choice' to be curious or having a strong sense of wonder, along with being glass half-full to the spectrum of possibilities is some of what you are getting at...
I don't understand what Van Inwagen's argument has to do with what you are presenting here. Van Inwagen's argument is about the necessity of moral responsibility, and the incompatibility of that with determinism. It makes (as far as I recall) no mention whatsoever of judgement of correspondence with reality, which is what are required to make scientific decisions.
If so, the fact that science requires 'choices' to be made says nothing about the necessity of free will to underpin science. What matters is how 'choices' are to be understood, not weather or not they occur in the practice of science. The equation of free will with choice seems to be a mistake.
