Dear Andrè (if I may),
Very clear and interesting essay. I find particularly inspiring your words, when you state: "However, we have to compare those predictions against what we observe, and predictions are never exact, even for deterministic theories. Experiments have errors. The constants in any theory are only known up to limited precision." I could not agree more! I think you might have an interest in having a look at my essay, where I introduce the possibility an indeterministic alternative to classical physics. These present remarkable similarities.
Concerning the Bayesian model, are you familiar with QBism as an interpretation of quantum mechanics?
Meanwhile, good job, top rate!
All the best,
Flavio