Your system sounds like the D20 compatible version of the Game of Thrones RPG (there are more than one GOT RPGs) that is now out of print. That might be what you are looking for.
This used to bother me as well. However, I started thinking of Hit Points as "stamina points", and it stopped bothering me as much. Essentially, I think of a loss of HP as the amount of effort the character had to expend to avoid the worst of the effects, resulting in bruises, minor burns, muscle strain, scrapes, etc. "Serious" injuries are in the form of ability damage, ability drain, bleed, and negative hit points.
Or at least, that's the "flavor" I'm using to justify a human having 6 times as many HP as a warhorse. Also, it helps rationalize why a 20 damage axe strike doesn't cause blood loss each round.
I have in the past also used a homebrew rule that may help with this rationalization. Instead of critical hits causing extra HP damage, I have them cause bleed. A x2 hit causes a 2 hp/round bleed. A x3 hit causes a 3 hp/round bleed. etc. It makes the heal skill more useful as well. Its a single change to the system, rather than trying to rewrite the combat rules, and may help.