> It is unsatisfying that quantum mechanics posits that particle states are fundamentally probabilistic.

You can alleviate this mostly by accepting the MWI.

Under the MWI, all the possibilities do occur, and the probability manifests because when you split into an infinitude of yous, each of them is just one you, and has no way of predicting which you it will be on the other side.

So the MWI makes the wave equation deterministic when viewed from the outside. The trouble is that we are inside it.

It turns out that God does throw dice - it's just that all the combinations come up at the same time.