You can replace "what would have happened" reasoning with "what will happen" reasoning. And "what will happen" reasoning is done by any model that can make predictions i.e. any scientific model.
I don't understand why you think that "exactly the same or exactly opposite" matters for this proof.

Of course, to calculate the probabilities (or expectation values) in the Bohm version of the EPR experiment (I assume we discuss about this most simple version which has been verified in various real-world experiment with and without delayed-choice setups and verified the correlations described by entanglement and the corresponding violation of Bell's inequality) you have to know the relative orientations of the polarization filters. You can make the setting randomly and in the delayed-choice way, but to be able to analyze the outcome of the experiment you have to put the information which actual setting in each event was randomly chosen.

For me, but here we again enter the realm of interpretation, the success of QT in the delayed-choice setting, is the strongest argument against naive collapse interpretations ever! What we observe concerning entanglement is precisely what QT in the minimal interpretation says: it's describing correlations due to state preparation before any measurement and/or (delayed) choice has been made; the correlations are not due to measurements/manipulations of the individual parts of the system measured.

You can look at experiment as consisting of two sides. One side is all the things done by experimentalist. The other side is done by theoretician who calculates prediction. Then the experimentalist meets the theoretician and after they confirm that they are talking about equivalent situations they compare two numbers - their results (experimentalist has some error margins for his number). If the two numbers are the same (within error margins) theory is confirmed.
Now if we look at entanglement experiment that way we could see that experimentalist does not need the measurement angles to calculate his number (to count the coincidences) but he needs measurement angle when he compares his result with theoretical prediction so that he knows that the prediction is the right one for his particular setup.

But you should compare apples with apples. Collapse interpretations are trying to say something about individual events while minimal interpretation speaks only about ensembles.
And it seems you could make your reasoning clearer by splitting calculation of prediction and experiment (with some theory independent data processing) into two separate parts. You have mixed together prediction with experimental result and speak about it as a single thing.

In the maximum entangled case two anti-correlated photons will always have the opposite state at the same detector angle. This equates to both polarizers Horizontal or both polarizers Vertical, you will always get hits on both detectors. (in the ideal sense) With the detectors 90 degrees offset (one H and one V) you will always get a hit on one detector and never on the other. (again, in the ideal sense, as if it were a perfect experiment with perfect components) If you give your photons an exact polarization angle (which equates to a hidden variable, and I don't think is realistic as far as experimental preparation is concerned) you could feed them through 45 degree offset filters and you would only get classical probability of hits on the detectors. QT predicts more hits of correlation and you would not be able to reproduce the result no matter how many extra variables you try to pin on the photons.

The actual physics is that a force is transmitted though the solid mass at most at the speed of sound in that mass. Nothing "relativistic" is occurring!

If polarizer A is 0° and polarizer B is 30° you get results for each side that come out to a difference of 25%. If you would have switched polarizer A with an orientation of -30° the results for side B would be the same and side A would have to come out to a result that was unknown, but different than B by 75%. If you would have switched polarizer B with a 0° polarizer and compared it to the result of what would have happened if you switched A with a -30°, you don't know what the result of A or B would have been, but you do know the difference would have been 25%. Can you see what I am getting at? The only way you can infer what the results would have been in the last case is if you knew the the input was the same for both sides A and B, and then you could have said the result for B at 0° would have been the same result for A at 0°; and from that information you could have concluded there is a conflict between the actual result and the what would have been result that leads to the spooky action at a distance conclusion.

It just hit me that the results for two polarizers at the same angle are always going to be the same result. So in the last case, I can infer what the results are for both A and B, and can reach the conclusion that communication between the polarizers is necessary for the results to be the way they are.

Thanks for the help! I won't say how many simulations I tried before reaching this conclusion, but as you can see from code snippet, it was more than 32.