Perhaps for the starvation death-loop, you could provide the player with the ability to ration food - let someone else starve to keep the Hunter-Guards alive until you return to equilibrium. Killing at random means I wound up, for example, rolling dead Hunter-Guards eight times until I wound up with none at all.
I know it doesn't make sense on a pragmatic level that Hunter-Guards can die of starvation too, but one occupation having privileges above another (like getting access to food first) doesn't make sense to me within the world Oil-Pit exists in; If you got food in case of starvation as a Hunter-Guard, wouldn't you idolize Hunter-Guards and want to be one to avoid a fate of dying due to starvation? wouldn't that create an imbalance at the heart of the group?
(Still planning on addressing those death loops at a later point though).