Perhaps he would be more convinced by one of deterministic quantum theories that exist today.
I am not aware of any 'deterministic quantum theories' now available? Quantum theory has equations that give probabilities between 0 and 1 for every event so it is indeterministic in that sense.
However, it is true that 'deterministic' is a rather leading term. Leibniz considered that the history of this world was absolutely determined from creation in the sense that the future can never be what the future was going to be in our universe. But he points out that this is a truism and is compatible with the
rules of possibility for any universe like ours being partly random. So it is not that we are uncertain that the future of this universe will be the one it will - we know that - it is that we must be uncertain exactly which universe we are in, until it has come to an end. This is a bit like Everett I guess.
But in practice what we mean by our physics being partly indeterministic is just this situation that Leibniz realised must apply.
I think infinities are an issue for indeterminism too. When an atom decays, it does so at a specific moment in time. However, if time is continuous then the moment of decay could never arrive without some reason for it to decay.
That doesn't raise infinities. It just means you have to use probabilities. It means that your equations will never give one absolute answer. But the math of quantum theory does that very neatly and the calculations are doable. There are issues with what is called renormalisation, but these turn out to be tractable. And running zillions of experiments has shown that the probability values predicted are accurate, as probabilities, to 18 decimal places.
The situation is certainly counterintuitive but Leibniz argues that our intuition simply cannot work in a mathematical theory without producing infinities that destroy the result
at the limit. That is to say there must come a point where there is uncertainty, perhaps at a billionth of an inch - which of course quantum theory shows to be the case.
Probability theory handles infinities of options very nicely. Interestingly one of the other things Leibniz worked out was how much insurance premium people should need to pay in for a viable life insurance arrangement. He did not construct a formal probability theory but he was one of the first to use the math of probability in a practical way.
It is my understanding that even this randomness can be explained if there is some statistical dependance with how measurements are made and the states of the particles.
I don't follow that.
Statistical dependence would be involving randomness surely? There have been suggestions that measuring conditions are somehow predetermined, I am aware. But the experiments using photons from distant galaxies seem to rule that out. (The measurements are 'chosen' by photons arriving from so far away no local correlation seems possible.)
It does not seem that superdeterminism is the most popular theory, however it seems to be rejected for its implications and seeming implausibility, not because the math isn't supportive.
I think there is some confusion over what is meant by 'superdeterminism'. I have had long conversations with physicists about this. If it means what Leibniz meant, that the future of our universe was always going to be what it will be, it is true by definition but does not stop the rules (for such universes) being truly partly random. Sabine Hossenfelder tries to grapple with this but I think she is still making the usual error in not treating time and space equivalently in terms of indivisibility within an excitation.
If you accept that every 'quantum' (field excitation) happens 'all of a piece' in time as well as space then the 'measurement problem' evaporates. The mistake is to stick to the idea that quanta 'progress through space' or 'move'. If they are seen simply as connections between spacetime locations of fields the answer to the superdeterminism issue is already dealt with. The creation an excitation occurs according to rules of probability given by quantum theory that involve and integration over a field domain extended both in space and '
forward' in time, as is clear from Feynman's simple account of QED. The field that throws up a photon in Andromeda already knows the absorbing conditions on earth when it 'calculates' the need to create such a photon. It is in the basic math of the theory. We didn't need the Aspect experiments to confirm that but people have such difficulty casting off intuitive realism (especially Einstein) that we went through that. And still people are puzzled when they don't need to be.