I noticed that, like myself, O'Neil concluded that each POF chapter has a world-outlook-mood as described in Human and Cosmic Thought. The first seven chapters follow the order of Occultism [0], Transcendentalism [0], Mysticism, Empiricism, Voluntarism [0], Logicism [0], and Gnosis [0].

O'Neil differs with me on the Part II chapters by following the same sequence from Occultism [0] to Gnosis [0] for chapters 8 thru 14. I reverse the sequence for the final 7 chapters beginning with Gnosis [0] for chapter 8 and ending with Occultism [0] as the mood for chapter 14.

Who is right, or is it merely subjective, or can both be right based on some further explanation as to how that is possible?

One difference could be that I concluded each chapter has an opening introduction that sets the mood of the chapter before the views are presented so I looked to this opening section to discover the mood. But the mood does permeate the whole chapter.