A similar, but simpler wound system I worked out a while back might be better for you. It basically turns HP into stamina and adds a Wounds system on top of it. Wounds don't have a penalty attached to them like exhaustion does, because that creates the death spiral, but they do make combat more lethal, even at higher levels. If using this, I'd recommend fully restoring HD after a Long Rest, rather than only half.
Creatures have a wound threshold based on their size category (feel free to modify the amounts, I never actually got a chance to playtest this). If your wounds ever meet this threshold, you die. When you reach 0 HP, or whenever you take damage while at 0 HP, you may choose to remain conscious and active or fall unconscious (Stabilized). If hit with a subdue attack that would put you at 0 HP, after taking any wounds you must make a Con save DC: half damage (minimum 10) or fall unconscious (Stabilized). While at 0 HP and active, you must make a Death Saving Throw at the end of your Turn, but if you took no action other than Dash or Withdraw, you do not gain any wounds by failing this save (you may still gain 1 HP if you roll a 20).
Wound Thresholds
Tiny: 3 wounds
Small: 4 Wounds
Medium: 5 Wounds
Large: 6 Wounds
Huge: 8 Wounds
Gigantic: 10 Wounds
Gaining Wounds
Being Critically Hit (not cumulative with % of Max HP wounds)
Taking damage from a single source more than 25% your Max HP
Taking damage from a single source more than 50% your Max HP
Taking damage from a single source more than 75% your Max HP
Taking damage from a single source more than 100% your Max HP
Taking damage while at 0 HP
Failing a Death Save
Rolling a 1 on a Death Save
Removing Wounds
Healing HP from a single source equal to 25% of your Max HP
Healing HP from a single source equal to 50% of your Max HP
Healing HP from a single source equal to 75% of your Max HP
Healing HP from a single source equal to 100% of your Max HP
Lesser Restoration option
Greater Restoration option removes 1d4+1 wounds