The BS AR reflectivity in polarization P has not been measured. But the calculated reflectivity is 1.3% in polarization P compared to the ~300ppm measured in S polarization. This would mean that the B5 beam amplifies by a factor 40 the relative contribution of polarization P to polarization S compared to what is actually resonating inside the interferometer. This means that the B5 beam polarization is actually telling us that there is 0.1% of the beam in P polarization, and that this changes during the lock acquisition by +/-250ppm. This is a more reasonable amount of P-polarization polution, but also it is much less likely to be an issue causing mystery noise.

This also helps explaining why the beam on the B5 camera has a cross shaped in single bounce. The cross shape comes from depolarization in the Faraday (and maybe also the polarizers of IPC2 on SIB1). And both the BS AR and the transmission of the pick-off mirror used by the B5 camera send mostly P-polarized light onto the camera. That pattern then disappears with the full interferometer locked, presumably because it looks like an order 2 mode and is not amplified by the PR+arm cavities, while the TEM00 is.

It also means that the B5 beam is a far worse candidate for the balanced homodyne local oscillator, as it is a pick-off of mostly the wrong polarization of light that is likely to have less well filtered input laser noise (frequency and amplitude) compared to the S-polarized light.