You guys are making it sound so complicated!
In my opinion, the beliefs that free will is compatible/incompatible with determinism (and eternalism) is based on a different definition of the terms. Hence the protagonists are simply arguing at cross purposes.
That's pretty much it!
What we mean by our free will is that we conceive some choices, and we say that "I made the decision". At any rate, the decision was made according to expectations you have about the situation, aiming for the best outcome (even if you choose to jump down from a cliff to prove me wrong, you did that exactly with the expectation that that action would be the action to make, in order to "prove your point"... oops)
And the fact that you can always view that process of "generating expectations" as a mechanical process, means you can have "so-called" free will, exactly as we experience it, inside deterministic worldview in completely self-coherent manner.
Determinist will say "I chose to do X because of Y", and by that they mean "whatever natural process exists behind my idea of "self", generated the reasons to do "X", and there was a subjective experience of that process".
A person who doesn't believe in deterministic world will say the exact same thing, but by "I" they just mean something partially or totally unexplainable. (If they were to explain I with smaller parts and definable behaviour, they would be determinists by definition)
So I don't really mind if by some definitions, someone chooses to see the automatic behaviour of carburator as an instance of a very similar circumstance/process as what is usually called "free will", or if someone wants to define a difference between those circumstances.
One meaningful difference one could make is that the carburator does not produce expectations based on an artificial world model; rather it is our world model that sees the situation as a "carburator doing things". From the point of view of the carburator, there can't really be said to exist a world conception that defines "self" and has ideas called "making decisions".
And then that argument can be easily dismissed by pointing out that it is not "really" a case of "producing expectations based on an artificial world model"; that's just a way of seeing the situation and in fact the expectations can be seen as arising from a mechanical process, of which there exists a subjective experience as if the expectations were based on the world model etc, yada yada, merry go round and so on.
Oops, sorry if I made it sound overly complicated myself