I see this as a bit of a once and done campaign as you would need to have the character in the dark about their actions. The whole character would need to be reinvented through the process of death, which makes this perhaps just an add on to an existing campaign.
I am thinking that the players would not just be zombies but allow their actions to move the character in a direction. Perhaps what they consume changes their undeath a bit for the good and bad. Maybe drinking live blood allows you to be more like the living, but with a price. Maybe consuming animal flesh makes you more like an animal and less thinking. I guess you get into the World of darkness area with humanity points a bit with negative consequences. But my focus is to end this where a World of Darkness game begins. you are not a vampire or ghost but you could become one.
You could even have actions drive your outcome , with stuff like hiding yourself away allowing you to become more and more able to hide until finally crossing over to being a poltergeist. The point is the confusion of not knowing what is happening and how the characters are being changed through their actions.