It seems to me that currently there is but 1 possible link.. for as we do not know in Onikakushi-hen if the disaster happened or not.
(however I am leaning to the fact that it didn't, I cannot support this decision based on any facts)
The possible influencial link I speak of is..
Rika's type of death.
Again.., I stress that since we do not know the outcome on Onikakushi-hen.., the possibility of her type death having any influence on the Disaster can then be compleatly comproved or disaproved.
On Watanagashi-hen / Meakashi-hen Rika takes her own life, this dispite under the circustances of what happened.., she commited Suicide and the disaster did NOT happen.
On Tatarigoroshi-hen / Himatsubushi-hen Rika is found murdered, and as she predicted herself, she would be killed.
The disaster happened.
This is realy just a long shot.., but currently it is was the only connection I could find upon when reading the outcomes..
It definitly lacks alot of detailed support, and unfortunatly I at the moment cannot give such; however.. I am in hope that once Tsumihoroboshi-hen ends we can come to a good conclusion on it.
At least this was worth it just to organize all the death's that toke place through the arcs