I may have a crack theory, originally building off something for the reincarnation topic, but I'll post it here.
The cycle of death and rebirth from the mountain's water is a huge part of Mt. Hikami's religion, particularly the emphasis on a "proper" death, which made me wonder why dying properly was so important, other than potentially creating a ghost. I came to the idea that if the cycle were to break, a "ripple" of that person's soul would be created; not a reincarnation, but someone spiritually linked to their previous life and its fate, being enough of their own person to make the decision to walk the same path (dying improperly) or correct it, allowing the cycle to complete.
Looking at known or suspected reincarnations does point to their original having died without closure in some way, like Kirie's Lover and Mafuyu, Akito and Kei, etc. The doubles also essentially correct what went wrong the first time. This ties into some observations I made while playing 5. During Chapter 13, after defeating Hiromichi in Yuuri's room, you can hear the sound of Haruka and Fuyuhi's song faintly in the background. The entire shop is empty, prompting you to examine the feed. The only ghost activity you can find is Kirika standing in the courtyard, which for some reason I associated with the song. Then a eureka moment.
I think Fuyuhi and Haruka are linked to the fates of Kirika Reizen and the shrine maiden, who are possibly their past selves. Perhaps similarly sharing romantic feelings, Kirika and the maiden were unable to be together due to the latter's duties on the mountain. For reasons I'll explain in a minute, I think the maiden was a Hakome, one of the weaker maidens who could only glance so much before being sealed, alone, in the caverns. Unable to live together or end it as partners in Ghost Marriage, Kirika chose to glanced by the one she loved, hoping that they would be together in the next life someday.
My headcanon about the song is that, like the Shadow Festival in the Minakami area, or the varying versions of the lullaby in 3, it was originally a song in the Mikomori region for lovers that was passed down and altered, losing most of its original meaning until it was sung by Fuyuhi and Haruka in their time, though originally sung by Kirika (one of the game notes does mention someone hearing a sound like a song, which couldn't have been F or H as it was seemingly written before they came to or died on the mountain).
Regarding those two, what happened with Chiaki and the group suicide set Haruka back into her role as a Hakome; taking in the deaths of her friends made her stronger, qualifying her for a reliquary. However, her heart wasn't full yet. I think while back on the mountain, possessed into acting as a maiden, Haruka summoned Fuyuhi, glancing her from afar as she reenacted their deaths, and later was successfully submerged. The illusion wasn't fake.
The explanation that the deaths were originally witnessed by Honoka, who is fulfilled by Yuuri in the present, is awesome and the last bit of the puzzle.