How about something along the lines of hit points are combat luck, stress, fatigue, ect... Include rules for wounds, balance what a wound does through playtesting but something along the lines of -1 to all rolls to start with might work. A character or opponent receives a wound when they are crit or when they drop to zero hit points.
Have hit points come back very fast and easy after every fight, have wounds recover with only time like maybe a recovery roll after a full days rest to see if they remove one wound. Rituals could be included to remove wounds as well wizards, clerics, druids, any spellcaster could learn said ritual.
The thing is hit points now that they are clearly not meat points, it is easy for all kinds of class or race abilities to recover them in combat or grant temporary hit points. This way the martial fighter types can have a rallying cry power and it is OK.