My opinion on the horcrux search is this
Someone said earlier that it's a game within a game and that's how we oughta look at it. Regardless of what we choose to do, how we interpret what went on during the search is part of the game as well. If I say ima visit the Owlery and I die tonight, it's up for y'all to figure out if I got killed because I was about to uncover a horcrux, or if I got killed in order to frame it that way, or if my death and the location are entirely unrelated. It's an info-related minigame if you will, and I do think we'll be forced to play it, because if this game's flavor is anything like the books, we need to find all the horcruxes or at least the majority of them in order to slay Voldemort.
Far as our strategy goes, I think that both not coordinating at all, and coordinating into the finest element aren't optimal. What I would suggest is that about idk, half of us explicitly split up in order to try and cover a good amount of ground, and the rest of us pick from the remaining locations. That way we got a good blend of coordination and randomization going, as well as giving people agency over where they choose to go, which in turn may be analyzed down the line as well. Lies will be told of course but that's just part of the game, that doesn't mean it's a waste of time or a poisoned chalice, we gotta take this horcrux search somewhat seriously as well.