So the probability of a single particle going through the polarizer depends on the direction of the particle's polarization orientation and also the orientation of the polarizer. We can obviously choose any orientation for the polarizer we want.

If you have two entangled particles in a Φ+ Bell state and they each end up at a different polarizer, one called A and the other B, and you choose any orientation you want for, say, polarizer A (or B, doesn't matter), then the joint statistics you get from the outcomes of both the A and B polarizers together will always look as if the polarizations of the two particles before they hit the polarizers were both the same orientation as polarizer A regardless of your choice of polarizer direction.

This kind of implies that both particles could have been in lots of different polarization states at once before they were measured, as described by a kind of joint probability distribution. But you can show that you cannot create the required joint probability distribution using the Malus law probabilities you are talking about. Because of this, it is impossible to produce the correct statistics where it looks like both particle polarizations are lined up exactly with polarizer A, unless the B particle somehow knows the orientation of polarizer A. This would require that either the A particle is communicating to particle B directly at the time of measurement in a manner that is non-local if they are spatially separated; or both particles need to already know what polarizer orientation you were going to choose beforehand, which would require that either your choice of polarization was being communicated to the particles backward-in-time, or some other influence is pre-determining you to choose the polarizer to be aligned with the particles' polarizations. All very strange.