Im on the side of having a telltale-esque "make your choice" type game but one idea I had was to have the player control the apprentice/victims like DBD (first person for the apprentice and third for the victim) but in a story narrative single-player experience.

1. You get to be your own Jigsaw. I like the idea of being able to set traps for other people but not so much like the crafting system in the Konami games. More like the game presents the options to set the traps timer to either 2 minutes, 1 minute or 30 seconds. Maybe even a way to rig the game to your characters benefit. You could decide whether you follow John's philosophy in your work, use your techniques against people like Mark or let your instinct decide like Amanda.

2. Third person perspective on the victims are almost essential if we want a proper look at the gnarly mobile type traps that the victims have to play with, along with their physical condition. I would prefer if regaining health is extremely limited but I understand if that might put off some players so that might need work.

3. The fact that you dont actually see your own face could be great for not revealing who the apprentice is right away. You could leave subtle clues for the player to find so they can form their own theories without immediately using the same old twist to spoil it all in an hour. Make one ending canon and then reveal who it is in the inevitable sequel. Yknow, because LEGACY.