Bell's theorem demonstrates that you cannot have a deterministic theory that would also be Lorentz invariant, that is to say, compatible with special relativity and the speed of light limit. The speed of light limit is very well tested over and over again, and no one to this day has ever been able to construct even a single mathematical model that could even approximately reconstruct the predictions of quantum field theory in a way that is deterministic. That suggests that any deterministic theory would actually make quantifiably different predictions than quantum field theory, and yet we don't have any evidence that its predictions are violated, and quantum field theory is verified to 12 decimal places of precision.

I don't really understand your point about the dice. If you have two "quantum" dice that are exactly the same, they are not guaranteed to land on the same thing, and that is precisely what it means to be nondeterministic, that even if all the initial conditions are the same, the outcome can be different. Yes, we cannot make the whole universe the same throughout the experiment, but to make sense of this, you cannot speak in vague philosophy but need to actually specify in mathematical terms what parts of the universe you think are determining the outcome, which, again, any attempt to specify such a thing would require contradicting the predictions of quantum field theory.

My issue with your argument is that, whether or not you intended this or not, what you are undeniably arguing is that all our current physical theories are currently wrong and making the wrong predictions, and they need to be adjusted to make the right predictions, and you are basing this off of what is ultimately a philosophical criticism, i.e. that it is not deterministic and you think it should be, without even having a viable model of what this determinism would look like. It just seems far too speculative to me.

Yes, you can always make the argument that "our old theories have been proven wrong before, like Newton's gravity was replaced with Einstein's gravity, so we shouldn't put much stock into our current theories," but I just find this unconvincing, as you can make this argument in literally any era, and thus it completely negates the possibility of using science to understand the properties of nature. Every scientific theory would have to always be interpreted as just something tentative that can't tell us anything about nature, because it's bound to be replaced later, and instead we're just left arguing vague philosophy not based on anything empirical.

I will readily admit that if I base my understanding of reality on our best physical sciences of the era, those can be overturned and I could be shown to be wrong. However, I still find it to be the most reasonable position as opposed to trying to "intuit" our way to an understanding of nature. The person who strongly defended the Newtonian picture of nature prior to Einstein was later shown to be wrong, yes, but he was still far more correct than the majority of those who insisted upon trying to derive an understanding of nature entirely from intuition/philosophy. I am with Heisenberg who argued that until we actually have any experimental evidence that violates the predictions of quantum field theory and can only be corrected with the introduction of hidden variables, then positing their existence is pointless metaphysical speculation, not derived from anything empirical.