Hippolyte,
One of the best wrestling matches against quantum theory I've seen! Excellent stuff. And of course I agree the conclusive question; "..quantum theory is more paradoxical than other physical theories. But is Nature itself paradoxical?"
However might there be a different possible starting assumption and mechanistic physical measurement sequence producing the data? Shockingly I suggest there might. Neils Bohr carefully made NO assumptions about pair morphology, but if we assume simple Poincare sphere vector distributions, and the same for polariser electrons, we have TWO distribution; polar curl and equatorial linear, going inversely to 0 over 90 degrees. Whats more, the change rates are Cos Theta Latitude (of the absorption interaction tangent point).
We now only need 'entanglement' as matching axis orientation angle, and vector addition in 3D, we can produce Malus' Law at the 2nd (photomultiplier) interaction, and NOT require non-locality! (think of it as changed ellipticity of re-emission, only the major axis triggering ONE channel, or 50:50 if circular polarity. I identify John Bell anticipated such a solution (touched on in this years essay but given in more detail last year). It was independently verified to violate bells inequalities by Trails computer code and plot.
Few seem able to follow this (DFM) process. I hope you can. Do question it.
But well done for your essay and good understanding of QM.
Very Best
Peter