I drew out some idea of how we might use a single OMC to clean both paths of the BHD after mixing, without being susceptible to polarization-dependent effects within the OMC. Basically, can we send the two legs of the BHD into the OMC counterpropagating. I've attached a diagram.
I think one issue would be scattered light, since any backscatter directly couples into the counterpropagating mode, and thus directly to the PD. However, unless the polarization of the scattered light rotates it would not scatter back to the IFO. And, since the LO and signal mix before the OMC, this scattered light would not directly add phase noise.
Maybe more problematic would be that if the rejection at the PBS (or the polarization rotation) isn't perfect, light from the LO directly couples into the dark port. Can we get away with a Faraday isolator before the OMC?