How about HP as breathe, as stamina, as your HP winds down you become more exhausted. You can't dodge anymore. You can't move fast enough anymore.
If it is explicitly stressed in narration and the description that HP grinding down is the player getting exhausted and losing their breathe than I think it would add an extra layer of immersion to the world that really only books and a few movies I think have managed to capture well. Players would probably be able to relate to characters who also get exhausted and tired and sore in a way that you don't really get from unstoppable murder machine people.
It also ties in really nicely to overall aesthetic and play-style of 'gritty' dungeon crawling.
As well abstracting HP into exhaustion allows you to neatly create a mechanic to deal with fatigue/encumbrance. HP just drops as you become fatigued.
Now this of course works best with Into the Odd's style of low hp auto combat that quickly wears you down and then is quickly replenished.
Not necessarily that groundbreaking, but maybe it'll give some one a good idea.