From what I understand, there isn't really reincarnation in this universe? Like, Fushi's creator says that it's theoretically possible if someone had a strong enough will, but it's never confirmed. Personally, I like to think that Hayase's lingering will does have some sway over her descendants (hence Mizuha's grandpa's obsession with their family legacy and Mizuha's obsession with Fushi), but I don't think her spirit has been reincarnated again and again this whole time.
It was pretty much confirmed narratively that all of Hayase's descendents with the nokker were her fye. Each time it reincarnate the old personality/memories are gone.
We saw Parona seemed to reincarnate as Hana with some similar traits. All of Hayase's reincarnations have her eyes. I also think they wouldn't choose paradise, yet since their spirits aren't around they were recycled into the next body. Each of them was their own person though, just the same fye. It's extremely unlikely Kahaku can come back unfortunately, because he did reincarnate.
I wonder if a fye can get it's previous body's memories though, especially if it were put in a copy of the body. Like if Fushi made a Kahaku body and say Mizuha's spirit was there, what would happen?
Im not sure about this but why are people saying the Hayase descendants are 'reincarnations'.. I think they are not. It is just the will of the knocker that was passed to them but they have diff souls..
There are some references here like Gugu's brother being reincarnated in the New Era. And he still have the same face and features. Since his sould has passed on to the 'paradise', he is able to enter the reincarnation cycle. I hope Kahaku will get reincarnated too.. it doesnt matter if he doesnt have memories of the past..