The HDMI Ouput Module is compatible with the P4P.
I just got my P4P. Upgraded firmware, got everything working OK.
Took the HDMI module out of my P4, swapped it into the P4P controller. Controller won't fully boot up - only white lights on the bottom. Tried resetting, re-pairing, resetting controller. Also tried swapping the HDMI module back to the P4 controller, and it works perfectly there. I even tried updating the software on the P4 controller to v1.8.0 and swapping the board back to the P4P, still no dice.
I'm waiting for the CrystalSky monitor, so no rush on the HDMI side, but it sure doesn't look like my particular HDMI board works in the new controller.