I did not see your email in your profile, but I will try to answer your question. I am not sure what the P2/P10 adapters are that you mentioned and I have not used the Sony ECM-44BMP with the Zoom H6, but it should work.
On the Zoom H6, you must attach the Stereo X/Y microphone to the top of the device to give you the 1/8" (3.5 mm) Line Input.
Plug the 1/8" plug of the Sony lavalier into the Line Input of the Stereo X/Y microphone on top of the Zoom H6.
Turn on Plugin Power in the Zoom H6 Menu.
Activate the Stereo X/Y mic by pressing the L Button next to the Channels (L, R, 1,2,3,4)
Let me know if you get it to work.