Lhv formalisms of quantum entangled states are ruled out -- not the possible existence of lhv's. As things stand now, there's no conclusive argument for either locality or nonlocality in Nature. But the available physical evidence suggests that Nature behaves deterministically according to the principle of local causation.
You've already agreed that the method of changing the polarizer settings, as well as whether or not they're changed while the emissions are in flight, incident on the polarizers, is irrelevant to the rate of joint detection.
The reason that Bell inequalities are violated has to do with the formal requirements due to the assumption of locality. This formal requirement also entails statistical independence of the accumulated data sets at A and B. But entanglement experiments are designed and executed to produce statistical dependence vis the pairing process.
There's no way around this unless you devise a model that can actually predict individual detections.
Or you could reason your way around the difficulty by noticing that the hidden variable (ie., the specific quality of the emission that might cause enough of it to be transmitted by the polarizer to register a detection) is irrelevant wrt the rate of joint detection (the only thing that matters wrt joint detection is the relationship, presumably produced via simultaneous emission, between the two opposite-moving disturbances) . Thus preserving the idea that the correlations are due to local interactions/transmissions, while at the same time modelling the joint state in a nonseparable form. Of course, then you wouldn't have an explicitly local, explicitly hidden variable model, but rather something along the lines of standard qm.