Blood Hunt - The Mori Gamble
I get that Mori's can be used to skip a hook stage, you put in less work and it promotes tunneling.
What if it's made to be extra work and promote interacting with all survivors to get a Mori?
If you've hooked every survivor at least once/every survivor has incurred a sacrifice stage, you can invoke a Blood Hunt on dying Deathhook Survivors:
For dying Deathhook Survivors, Blood Hunt is an option in addition to pickup for the Killer (uses the same key as Kill, and if the Survivor is able to be Killed by your Hand at the moment via a Perk/addon the Kill prompt will override it).
This will cause the Killer to perform the hatch close animation (for sake of reusing assets). The dying survivor will then be healed completely and hastened for a duration. If that survivor is put in the dying state again, they can be Killed by the Killers Hand.
"Run"
Edit: The Killer should probably be rooted/prevented from performing actions for a couple of seconds so they couldn't take advantage of any insta-downs/powers/get a hit in immediately.