As for Battler's sin, im thinking in some kind of butterfly effect. There is evidence to think that its a promise in EP5 when Beato calls him a liar and Battler says "i dont remember promising you anything" or something like that.
We know that it was something that happened 6 years ago. Battler remembered that the shrine was not there anymore in Ep2, right? so we can assume he was in the island 6 years ago.
What do we know about Battler 6 years ago? I think its written in an Episode that he was interested in Shannon b/4 right? In EP3, the line that Battler told Shannon 6 years ago, could it be possibly that it was a promise? "I'll be back, <see you again>. I'll come to greet you riding on a white horse".
Obviously he didnt come back for 6 years, Shannon ended up with George. Eva didnt like this. Shannon made this illusion of the witch, the illusion told her to break the mirror to be happy with George and she did it. Kanon was hurt indirectly coz of Shannon's relationship with George and the illusion of the witch. Because of Shannon and George's relationship, Jessica ended up falling in love with Kanon and i could probably go on and try to involve every1 in the island coz of Battler not coming back to Shannon, and Shannon and George getting together.