Hm. I'm having a hard time putting into words down precisely what I take issue with here. I think it's the implausability of such a "church". I think it's because it's not so much a "church" as a philosophical get-together. If I get your gist, the theological-metaphysical theory here is that all things are a part of the Truth and are all equally legitimate, so the goal of the priests is to gather as much knowledge about "other" religions as they can (if "other" is the right word here, since the implication is they're all part of the same metaphysical idea).
That in itself is a nice idea, and I'd like to see that run. What I'm kind of bogged down with is why these priest-philosophers would bother pretending they're organized together. You pretty well state there's no central authority, or really any central tenet aside from "there is no one way". If that is so, then why are they going around Speaking/preaching these different ways? And even if they are, why come up with the circles and ranks? Given their ultimate goal (Oneness), the ranks and organization, scant as it is, seem to be ancillary at best and a stumbling block at worst.
If I'm missing the gist of it, please say so. But I have a hard time finding the need for the organization. The "these Are Our Churches" codex seems mostly just a freetext for religious ideas. That's fine and well if that's the case, but it seems a merely a meager justification for the Church of The One to exist. In terms of a unifying church for all faiths, I just don't buy it.
All that said, the idea of The One philosophy as a theologically underpinning is interesting, and I'd like to see more of it fleshed out. I'm counting myself as "not getting it" and will spare you my vote. I'd like to read more about it, however, just with a more engaging explanation for it.