I think this sounds awesome. When you say you want to avoid the bunker scenario I think of Resident Evil: Apocalypse where Alice meets up with that train of refugees. Which I think is what you're going for, you want them to be a group trying to survive together constantly on the move in world of limited resources with threats abound. But I don't think you're crazy and I think it's doable but I also think it would depend on group size and the writers you get. But I am interested and this one character I've had in my head forever sounds like she'd be a good fit if you did start a game like this.