Although it seems whoever solved the epitaph is compelled to inherit Beatrice’s name, and complete the murder ceremony. So maybe this is a “fool’s gold” solution, and there’s another “true” solution that stops Beatrice forever?
Well I guess that’s what Battler is trying to do.

Obviously, the story is magical—a Groundhog’s Day murder mystery. But that’s also a postmodern literary device. At its most fundamental level, you aren’t meant to explain how time loops happen. You’re meant to discover who wants to kill the Ushiromiya family…….I think?