Is quantum randomness just epistemic uncertainty of the microstates of macroscopic systems? As far as I can tell, randomness in QM occurs when a classical measurement is made.  Classical measurements involve macroscopic systems.  We cannot know the detailed microstates of these systems.  How can we tell that the random outcomes of quantum measurements are not related to the details of the measurement device?
The hypothesis I’m entertaining goes something like this: The laws of physics are quantum mechanical, and described by deterministic unitary propagation. [and] The apparent randomness that occurs in classical outcomes is due to the fact that we don’t know the exact microscopic state of of everything that comprises the experimental set up.
 A: Quantum randomness is not just epistemic uncertainty of the microstates of macroscopic measuring devices.
Or at least, since it's hard to completely logically disprove almost anything, it might be better to say that the price we would have to pay for accepting the above hypothesis is enormous.
Why? Let's consider the Bell experiment, where the two entangled particles are sent to the opposite sides of the galaxy, and let's examine two versions of the hypothesis:
Hypothesis 1. The result of measuring each particle is fully determined by the state of the apparatus interacting with it, independently of the state of affairs on the other side of the galaxy.
Then there would be local hidden variables (namely, the exact state of the measurement device) that would determine measurement outcomes. But Bell's theorem rules out local hidden variables, if the predictions of QM are correct.
So the price we have to pay for accepting this hypothesis is having to deny the predictions of QM.
Hypothesis 2. The result of measuring each particle is fully determined by the states of both apparatuses.
Then let's fix the state of the apparatus measuring particle $A$ to be $\alpha_0$. Then Alice's result (she measures $A$) is a function of $\beta$, the state of Bob's apparatus. Suppose some state $\beta_{up}$ results in spin up for $A$, and $\beta_{down}$ results in spin down. But that means information about which of these two states Bob's apparatus on the other side of the galaxy was in is now encoded in the result of Alice's measurement. I.e. information travels faster than light (even if it's hard to extract it)!
So the price we have to pay for accepting hypothesis 2 is having to deny relativistic locality.
Note: Relativistic non-locality is different, and far "worse" than the usual quantum non-locality, aka EPR/Bell-nonlocality, aka "spooky action at a distance".
A: One needs to interpret the probabilities one gets from quantum mechanics. Because of Bell Inequality violations, we interpret them to be fundamental rather than related to ignorance. This interpretation carries over to the cases where there are no such Bell-violations issues. You could choose to intrepret the probability in such cases to be due to ignorance, but you would need to have just the right microscopic states and interactions to match the quantum probabilties, and in addition that whenever the situation does probe locality then, by cosmic but certain coincidence, the fundamental (non-ignorance) probabilities arise. That's... a rather convoluted philosophy. Better to just accept that the probabilities are fundamental as a general rule.
A: Muon decay is a case where there is randomness, an individual muon’s lifetime as well as the details of the decay products, but where no interaction with a macroscopic system is required.  Muons are interchangeable and have no internal structure, so the fact that different instances decay differently is intrinsic quantum randomness.
(Though you can start to go down the “if a muon passes through a forest, and no one detects an electron, did it really decay?” Line of thought).
