I've made some changes to various elements of hit points in my historical game. Firstly, no one rolls them; everyone gets max hp for their HD at 1st level, and half HD for every level thereafter.
Secondly, and more significantly, I'm borrowing some stuff from 4e to make some simple conditions, that being Bloodied.
Record your Bloodied value underneath your hit points; this is equal to one half of your full hit points. The first half of your hitpoints represent brusing, minor fatigue, minor cuts and grazes. Drop into the second half (Bloodied) and you're into major fatigue, heavier brusing, more serious cuts, muscle pulls and so on, which give a -1 to hit, Proficiencies and saves and movement is reduced by 30'.
Hit zero (and up to negative your Constitution score) and you're in danger of going unconscious, having to make a Fort (Poison and Death) save every round to stay with it. Even then you're at a -2 to hit, Proficiencies and saves, and movement reduced by 60'. Fail a save or drop below negative your Constitution and you're unconscious (and we get into Mortal Wounds).
Thirdly, healing is changed. Primarily by adding a level link to natural rates.
Natural healing is equal to half your level in hp per day. If this is less than 1hp, then you take a number of days equal to that fraction to recover one hp. This is halved if a character is Bloodied (once you are above ½ maximum you return to the normal rate). This is doubled if under the care of someone with the Healing Proficiency. Furthermore, for every week of complete rest (no major exertion such as combat, running, swimming and so on), you recover an additional amount of hit points equal to your Con bonus.
Note that the healing times required to return to 1hp from the Mortal Wounds table still apply.
Fourthly, I'm thinking the spell-like effects of the Healing Proficiency only work when treating Mortal Wounds. They don't give insta-healing. Wounds recover with time, care and attention, not some lucky first aid. Essentially they represent surgery or some other intensive treatment on someone critically injured.