I don't see how the 'computable' part is relevant in regards to free will. You can write a program that outputs random numbers that it reads from some source, and you can simulate it by writing another program that outputs random numbers from the same source. The two equivalent programs will generate different numbers, but that doesn't mean they had any choice over the numbers they printed.
> Recomputing with different human shows that different choice was possible in principle.
Recomputing with different human is equivalent to creating an impossible universe. It's impossible to have two different people in the exact same situation at the same point in time in the same deterministic universe. The very action of pausing or modifying the universe from without would make the universe non-deterministic.
> And because running the simulation is equivalent to letting the simulated human to live that means we do not predict, but merely observe the choice.
Who's choice? If the algorithm is making the choice then the humans simulated by such an algorithm would not have any more free will than a video game NPC.