Neat concept.
Honestly, Zombies are a bit over done. Maybe consider different monsters to hunt? That could lead to more interesting dishes in the long run.

Imagine: Chimaera Three Spice Blood pudding, Vampire Hot Wings, Frozen Strawberry Medusa Snakes or Cyclop Gaspacho. Lots of possibilities.
I really like the Hunting/Managing parts. They seem more fast paced and interesting. I'd consider diminishing the importance of Butchering/Cooking. Plus to translate such high-concept mechanics such as cooking, a lot of effort would have to be put into making it work effectively.
Hunting could be like an overhead adventure (think Zelda/Pokémon). Before going out, you would have to select specific weapons to counter effectively different types of targets, or like you said, the ingredient quality would suffer. Maybe just use large areas interconnected by a world map that slowly unlock itself. Players could eventually hire employees and send them out on missions.
Managing could be like an hybrid harvest moon/slower paced diner dash. There could be a day/night system that the player could decide. Your restaurant could be even specialized in breakfast, lunch or supper!
I need to stop wanting to write about it! Yeah, it's a cool concept worth developing.


