This part is fishy to me. Shanon escapes the next room over, then proceeds to rescue Battler as Kanon. But her method of escape was still the window, which means the blue truth Gaap spoke did end up being used during the wedding ceremony. Yeah, Erika agrees to remove the seal, but Beato still needed it to be removed.
As for this part, Beato still needed to solve the logic error before presenting her own mystery. Although Lambdadelta was the one it was presented to, she was still required to have solved it.
Edit: I just thought of another question, though this one’s up for interpretation more than anything else: Did Erika arrive at the truth at the end of episode 6? After she loses the dual with Beato, her last measure of resistance is to introduce herself as the detective and the 18th human. Why would she say that if she had no doubts on the number of people on the island? She asked this after realising that multiple truths can exist in tandem and has a realisation about the nature of the world. I think she said that to clarify, at the very end, if what she’d just come to realise was the truth, and Battler and Beato confirmed it.