What I'm saying is that it's a hint of absolutely nothing. Deterministic systems can very easily produce deterministic large-scale behavior, and randomized systems can also very easily produce deterministic large-scale behavior. Since the large-scale behavior is the same either way, it gives us no predictive power over its ultimate cause, in the Bayesian sense.
> That's still deterministic. Sure, there may be some influence from quantum effects which then are amplified, but the dynamic of the chaotic system itself is still deterministic.
Your argument is that because we see "determinism falling out in the end", we should also expect "determinism at the root". But I argue that in the real world, we don't even see "determinism falling out in the end". On short timescales, computers appear to simulate finite-state machines, and the Earth appears to move in a steady pattern around the sun. But looking further out, the computer ultimately turns to dust, and the Earth wobbles out of its current path, thanks to the chaotic dynamics of the solar system. That doesn't sound very deterministic to me, unless we baselessly assume a priori that they have a deterministic cause.
What determinism do you argue does truly fall out in the end?
> That's not really true. "identical speed of light for all observers" is an observation which was replicated quite often. SR is a way to explain this observation, but there before SR Lorenz already had a different model explaining it too. SR won, because Lorenz used an (at the time) unobservable "ether" and Einstein argued that its better to use Occams Razor and throw this "ether" away.
In that case, we have two different interpetations that yield the exact same outcomes. Thus, I'd say that they're really just two different descriptions of the same model: they're equally correct, and Lorenz's description is just dispreferred due to being more difficult to work with.
> This in all contradicts SR, so maybe SR is really wrong on a global level.
There's nothing in SR that says that "most" matter can't follow the same reference frame. It just says that your reference frame has no bearing on the laws of physics you perceive, contrary to older models of the ether.
As I said, we already know that SR is wrong in that it doesn't predict any of the effects from GR, cosmology, etc. It's not an end-all-be-all theory of everything. But it doesn't stop it from giving good predictions for most places in the universe.
> Which in turn would allow a non-local, realistic interpretation of quantum measurements because without SR simultaneity could be back on the table.
You can do all that today, by specifying a reference frame that you want to consider. After all, that's how QFT does it, since it's mostly concerned about local effects. But you won't get different results from what SR predicts (in particular, the physics won't change if you look at the same system in a different reference frame), except in the circumstances where we already know it's incomplete.
Mechanics is fully deterministic. The question is if there is some kind of "QM random generator" which mixes into this, making things nondeterministic in the end. But it's possible to separate both and the "big clumps of matter" part is fully deterministic then because decoherence generally happens so fast that it doesn't matter. You need to prepare systems quite carefully to mix quantum randomness into it (like in Schroedingers cat for example).
> In that case, we have two different interpetations that yield the exact same outcomes
Only for "harmless cases". SR allows lots of strange stuff, especially if combined with gravity. Closed timelike curves for example.
But if time is absolute and only slowed down for objects moving against this background, then closed timelike curves couldn't exit. Also the trick with Kruskal–Szekeres coordinates wouldn't work anymore because switching time and space would by unphysical. This way we wouldn't have to care about the singularity (at least in Schwarzschild BHs) anymore, because space would cease to exists behind the horizon of a BH and there would be no Singularity.
> You can do all that today, by specifying a reference frame that you want to consider
But that wouldn't work with measurement of entangled object, because there would be no way to define an absolute frame in which the change of the wave-function into an eigenstate happens, it would always depends on the frame of the observer. QM requires that the change happens simultaneously, but SR doesn't allow simultaneous events.
Of course the problem with all of this is, that in the moment I can't see a way to do experiments which decides if there is absolute time or if the SR is correct.
If the planets they visited had much lower gravity then earth this may be possible, but this wasn't noticeable or talked about. And even on Mars you need much more fuel to get into orbit than could be stored in their tiny ship.