I am considering the following:

As it stands, if you're knocked unconscious but stabilize, you will gain your hit die per hour until you regain consciousness and continue to heal to full without any further interaction. If you were critically hit, an untreated wound will scar.

Thoughts:

This seems pretty odd to me that you're cut up to within an inch of your life and fully recover after a nap.

Considering:

The med-kit is not expendable as it stands, and has no set number of charges. So if at least one other party member is awake, they can go around and treat everyone's wounds, this would be automatic. So I would like to say, untreated wounds at least heal more slowly. I would accept that you could regain consciousness, so -HP will restore at the hit die rate, but once conscious, untreated wounds would naturally heal at 1/4 the rate per hour not less than 1HP rounded down.

Your thoughts?