Ever since hearing the hypothesis here that Maya is an angel or some other "fallen" element of the structure surrounding Akira's world, I have found it quite compelling. A lot of elements seem to agree with this line of thinking.
To me, one of the most intriguing lines in the entire game is spoken by Maya on the beach after her near-kiss with Sensei, just before encountering Ami and Ayane: "What am I doing here?" When I read that, I thought immediately that she was questioning some choice she made in the past that led to her being "here" in the looping world. If there are other takes on her mood just after Touka's interruption, I would love to hear them.
I concur with the suggestion that the resemblance we see between certain supernatural elements and Ami or Maya should not be taken to be a true thing. As we well know, everything hinges on perception. I believe that the further Akira's experiences stray from the day-to-day happenings in Kumon-mi, the less reliable his human perception becomes. Entities like youdidit, amiokay, Moyo, and even Nao, do not exist in the base, physical world.
We simply do not understand the true form of these semi-divine "cogs", let alone the relation between that and what Sensei sees when he is given an involuntary glimpse into their worlds. It seems reasonable to assume that the entities which resemble Maya share some sort of essence with her, and that the xoanon is somehow connected to Ami, but there's really nothing we can say for sure. Whatever the Wishing Well's library is, it's not an indoor swimming pool.
On the suggestion that Maya is still withholding information:
m "Despite my tendency to do so, I understand that it is typically impossible to predict the future. What {i}is{/i} possible is creating objectives or goals or...places you want to end up."
m "{i}That{/i} is what I’m doing right now. So please forgive me if I wind up leaving you out of those places if I’m unable to make enough room for you."
Perhaps these lines suggest that she actually has an idea of how to create a place she wants to end up, and a sense of how much room she might be able to make. Even if she's lost, it seems that she's not nearly so lost as the others.
This is a meandering post, but I have a final thought about the Original Sensei Love Squad. We understand, both from the author's statements and from the story itself, that Ami, Ayane, and Maya are in some sense the most important characters besides Akira. I believe that Ami is not real, or at least in some critical sense is less "real" than every other character. Conversely, I believe that Ayane is more "real", more grounded in some deep truth, than any other girl. I'm not sure about Maya, but it's clear that she is separate from the world in a distinct way, despite being a part of it.
A pithy summation of the above idea might be: Ami is unnatural, Ayane is truly natural, Maya is supernatural.
