Can you elaborate on this part?
I understand relative channel phase in a stereo system but I have a feeling you are talking about absolute phase from the original studio performance - which I don't know if there is a way of determining on a reel to reel tape, mono or stereo.
I guess I should explain that the tapes I am referring to are 2 track mono tapes that have only one channel per track, and must be flipped over to play the remaining material.
I am not sure what phase you would call it, I can only explain what is experienced when it is heard.
When I wrote about the reason for reversing phase to hear the mono correctly, I was referring to what is similarly experienced when playing a mono LP with a mono or stereo cartridge, but played back through a stereo system. I may not know the terminology to explain it, but without reversing phase either by a switch on the pre-amp, or reversing phase on a speaker cable, you end up with a wide image spread between the speakers, but when phase is reversed, the image solidifies into a single point between both speakers, and this will give you the illusion of a single speaker playing back the material. Just like you would get if you Like you are listening in mono. If you have stereo a test record with a phase test, you will experience the same thing in stereo.
I have no idea what will be heard with the TP's mono tape. I do not know if this effect can be changed by having a double mono signal.