mind expanding on the cuckoo bit? are you saying Ami isn't actually Sensei's niece/maybe daughter? or isn't actually Sekai's daughter?
Ami existed as a normal child at some point. Regardless of what else is actually true, I'm certain of that. Whether that was the child of Teacher/Sekai and Nozomu or the child of Teacher/Sekai and Sensei could be a coin flip.
But there are a number of traits about her that stand out.
1) She's behind literally every other girl in physical development
2) It's hinted that she's infertile
3) Most of the time when she shows up in Happy scenes, she's a mangle
4) Her head literally falls off in the sex dream that opens the game
She's trapped in the body of a child, with no signs that will ever change.
The implication is that Ami died in the car wreck, which would mean the version of her we know is either a reanimated corpse, a ghost, or an imposter.
I'll admit I'm bringing more information about cuckoos into the theory than is given by the game. But for most breeds of cuckoo, they're not just hatched in another bird's nest and cared for by a non-cuckoo. They literally instinctively destroy the other eggs in their first moments of life so that the mother bird can only care for them. And that feels waaaaaay to on the nose to not be something with regards to Ami, who has hinted at physical harm coming to any girl who gets close to Sensei and constantly insists that Sensei should spend every spare yen he has on her.
It's a theory -- and probably not one that would hold up perfectly under scrutiny, so it might just be a metaphor.
Also -- I don't mean a literal cuckoo. She's not a bird in a literal sense. I think when she died, one of the gods started keeping her alive to use her as a tool, letting some part of her have nominal control so there's a recognizable personality present, but the way she acts makes it very clear that there's someone else behind the wheel at times.
) which seems to be that God goal, so unless some MASS RAPE happens i think we are a little far from the dark route 
