Remember the Detective's Authority. Whatever is witnessed by the holder of the Authority is unquestionably correct, as well as any scene that takes place before everyone reaches the island, so long as its not being told to us by a character. So everything Battler and Erika sees are reality, and every flashback is real. So since both Battler and Erika see Shannon and Kanon, and since the objective flashbacks show both Shannon and Kanon, neither of them can be outright falsehoods.
Also check out my comment, I updated it cuz I posted too early by mistake, I got a lot more thoughts
Oh yeah also, everything Will says is true. Will just outright gives you the solutions. The question is, what does it mean? That's what you must find out, what he's saying means.