One thing I've never understood about interpretation of quantum entanglement experiments: Based on what I've learned of these experiments, it seems to me that the least mind-bending interpretation is that the entanglement event results in two particles that have some complementary property k (i.e. one particle has k and the other has ~k) and which one of the two, k or ~k, is had by one of the particles is unknowable…
Incidentally, I'll mention that your argument is essentially what Einstein et al were arguing for in their famous EPR paper. The fact that it's even possible to rule out local hidden variable theories is highly surprising, and is what makes Bell's discovery (30 years after EPR framed the problem) so monumental.