Jon - as I've mentioned before, I have made a study of auditory neurology and experimented with who hears what how. I would say that you 'get it' and in a manner that was formative to Thiel taking on the challenge of coherence way back when. We experienced and observed not only your "relaxing", but also emotional, memory and other musical connections in the coherent presentation which were not present in the phase-time-scrambled (normal) presentation. So, as a subject, your experience would have supported our study, even before we knew what we were studying.
One reason "it" is hard to explain is because "it" is not analytical. In fact the analytical brain prides itself at the descrambling task and a different kind of pleasure built around that cognitive success of restructuring a cohesive sound from its parts. I am drifting toward epistemology - how we know what we know - which is via very a broad count of different mechanisms. I say that the phase-time thing connects us to the music in a more direct, primal, whole manner. And you are experiencing that as relaxing. I call it 'coming home'.