I've been musing on the rules of the game lately, and I had an idea about what Meta-Beatrice's motivation might have been in getting Battler to play this game with her. I don't really have much supporting evidence for it yet, but I'd like to ramble about it a bit and hear what people think.
Beato wanted Battler to reach the truth, but she drew out this game as long as possible, tried to deceive him, and made both him and herself suffer in the process. She wanted the culprit exposed, but for some reason she wanted Battler to drag himself to that truth in spite of her efforts to hide it. If she cares about the family so much that she's willing to take the blame for all of their sins, why did she try to protect the culprit who murdered all of them? And once Battler learned the truth, why did he join her in trying to hide that culprit's identity and forgive her for all of her own sins? Or to put it another way, is there a particular person who Beato and Battler would behave this way for, if they were the culprit?
My idea is: no, there is no such person. The clues Beato provided in the first four games do not single out a specific culprit, but rather allow two or more possible theories, each with a different culprit. And that's exactly the point.
According to the rules, many different possible solutions can exist as long as they don't violate the red truth constraints. For example, there may be an ultimate solution in which Shannon is the culprit and Kanon is innocent, and another solution in which Kanon is the culprit and Shannon is innocent. Let's say these are the only two solutions permitted by the red. In that case, who is truly guilty? By Battler's logic, until the cat box is opened and someone's guilt is proven, they're both innocent. But in that situation, who would dare swing the red sword and condemn someone they love as a murderer?
We already have plenty of quantum physics in our mystery, what with the many-worlds interpretation and Schrodinger's cat box, so let's throw in another term. Entanglement, a state where two particles are in related but unknown states. Say, one has spin up and one has spin down, but you don't know which is which until you open the cat box. Up or down, innocent or guilty. Beato has the power to decide which way it goes, but she loves everyone too much to make the decision herself, so she tried to get Battler to do it for her. She wanted him, using the blue truth, to force her to pick a culprit.
But in the end, Battler reached the same conclusion that she did. He understood why she hid the truth, and he could hardly condemn her for refusing to damn a loved one; he didn't want to do it either. That's why he forgave her, and switched to her side for the sixth game. But Virgilia understood that as long as they didn't choose a murderer, there would be no hope of catching that murderer, and no hope of releasing the other sixteen people from the island. They would remain in purgatory forever. It's like Maria's fairy tale about witches from EP4: one must be damned so that everyone else can be saved.