Besides the creation of angular momentum, would you say we could also characterise the difference between PR and QM correlations as either
giving us inconsistent results?
or perhaps simultaneous answers to incompatible questions?
I'm not sure those in quantum information theory (QIT) would agree with either characterization. The PR correlations satisfy the no-signaling condition, so as far as QIT is concerned they are legit. That being said, I have had many exchanges with people in QIT and none of them dispute the fact that superquantum correlations violate the conservation principles introduced in my Insights. And, most agree that those conservation principles are legit. However, they are looking for something "more general" to explain why the PR correlations are not physically instantiated. We address their desideratum in Reference 1
There's also the principle of information causality, the PR correlations allow one to transmit more than n bits of classical information with an n bit signal.
The pedagogical advantage of the PR correlations is that things like the uncertainty principle (or even stronger results like the Colbeck-Renner theorem) fall out quite easily from them in a way that is much easier to see than for Quantum Correlations.