What if hit points (F20 style) didn't decrease with each hit, with the possibility of death at zero? Instead, what if they started at zero and accumulated? The player with the lowest score at some milestone is the winner!
Everyone's a tank. Everyone can leap headlong into battle and not worry about dying. You get to keep playing your character. The reward is something else; a magic item, the glory of victory, the singing of songs, extra XP, whatever.
You might like to add something to account for toughness. Maybe fighter types can reduce incoming damage by some amount, whereas less physical characters take the full force. Do it if you think the armour rules you have aren't working well enough.
It'll be just like golf. Lowest score gets the blazer.