Polarizing filter that fits inside bayII lens hood?

I'm looking for a polarizing filter to use with my Rollei 3.5E type2 but I'd like to get one that is compatible with the Rollei bay II lens hood. I've learned that I can either get a bay II Heliopan (since the Rolleipols often have problems with foil separation) or an adapter and a 39mm filter (Heliopan or B+W have my preference).

Does anyone use a polarizer in combination with a lens hood and if so, which brand/model filter do you use? Or if you own either the Heliopan bay II or 39mm filter, could you measure the outer diameter for me? (I have already emailed Heliopan but have not received an answer yet). Also, does anyone know if there is a real difference in image quality between the normal and PMC coated Heliopan filters?

Thanks in advance!

I'm curious why you are committed to the Bay II hood for using a polarizer? You can't take the filter on or off without removing the hood, you most likely can't see an index mark for rotating it while in place with the hood.

I'm assuming that you will put the filter on the viewing lens, find alignment, then transfer it to the taking lens.

I used a Bay I to 52mm adapter when I used a polarizer with a Rolleiflex. I already owned the 52mm filter. I used a round lens hood attached to the polarizer for this setup. Although both the 52mm adapter and the hood overlap the viewing lens, I don't notice any problems with focusing and framing.