You're right, it's a fairly direct route from the assumption that there is perfect correlation at identical polarizer settings to the conclusion that the local realist must believe that the correlation is linear. But ThomasT does not agree with this fairly direct line of reasoning, so I'm trying to convince him that it works.
If I could persuade ThomasT of this, I'd be done.
But that just has to do with practical experimental limitations. The point I'm arguing with him about is whether someone can believe that all the predictions of quantum mechanics are correct and still believe in (non-superdeterministic) local realism. I'm trying to show that the answer is no, because one experimental prediction of QM is perfect correlations at identical polarizer settings, from which the local realist is forced to believe in a linear correlation relationship, which is in contradiction with another experimental prediction of QM.
I agree that this is the point of contention, but keep in mind that he thinks a local realist can believe in the nonlinear correlation given by Malus' law, while at the same time also believing that there is perfect correlation at identical settings. I hope you agree that he's wrong on this point.
Out of curiosity, which experimental loophole of Bell tests do you cling onto? Detector efficiency, communication, freedom of choice, or something else?