It seems I've been mistaken, it is ending 8, "Memories of That Day", which triggers the second playthrough and change in title screen. You can only get the normal (and true) end on second playthrough still after getting ending 8, and the true end additionally requires you to have seen ending 2 "To search for Toko..." and not having slept with Ayumu or Yukiko. The true end however does not require the normal end.