Add another divine smite in the form of inflicting some duration of temporary intrinsic hunger. It’s a nice counterpart to your god filling your stomach when you pray (which is inaccessible if you get smited with hunger, since the god has to be angry).

This may be tricky to balance because either it happens early in the game and there is not sufficient food, making this a death sentence; or later in the game and there is so much food that this is a minor annoyance.

Eating a bag of holding confers temporary intrinsic hunger, and eating a bag of tricks confers temporary intrinsic aggravate monster.

Famine’s attack gives you some amount of temporary intrinsic hunger in addition to the direct damage to your nutrition it already does.

Non-cursed rings of hunger don’t drain excess nutrition when you are Hungry, and slow digestion rings don’t slow your digestion when you’re oversatiated.

The hunger property, instead of doubling hunger rate, halves any nutrition you get from any source, making it marginally more useful for eating large corpses. (This should probably only be granted by the actual hunger intrinsic, i.e. the ring of hunger, as opposed to other intrinsics like conflict and regeneration that burn through nutrition fast but aren’t explicitly about being hungry.)