Random theory time:
I'm not sure if anyone has mentioned or theorized this before, and it definitely comes out of left field, but anyone else think that Geoffrey might actually be the third god/Pareidolia? Ayane's butler.
Geoffrey can mean divine peace and is related to Godfrey, and has a reason to want to aid Sensei while not actually liking him or being on his side. Ayane loves him and Geoffrey seems to be one of the only people that cares about her, and pays attention to her. Not to mention, I can see why a butler would be "concerned", and Pareidolia could easily be a code name, which based off Geoffrey's apparent life, it wouldn't be surprising if he's had code names before. I also recall Geoffrey and Pareidolia both mentioning/being mentioned to want to meet/get a hold of Sensei at some point. (Albeit it's been awhile, so could be wrong)
Not much credibility, but it did seem like a possibility.
This and a theory that Sekai might actually be some entity that created and became this world when Maya prayed for anything to resurrect Sensei after he killed himself for knocking her up, have been on my mind for a bit.