I've had ideas of my own, obviously. I'll put together another idea here, based on what I've written above. (Note: Largely written on the fly, with no guarantee of appropriate balance.)
When you take damage (treat multiple attacks separately) greater than (Con modifier + Level/2 + Hit Die size), make a Con save against a DC equal to half the damage done (minimum DC of 10) [same as a Concentration save]. If you fail the check, you take a minor injury.
You cannot have more than two minor injuries at the same time. (IE: Ignore any further minor injury checks if you already have two.) You heal one minor injury (your choice) per long rest.
Example minor injuries:
- Sprained ankle. -10 to speed, and disadvantage on athletics and acrobatics skill checks.
- Rung Your Bell (headache). Disadvantage on Intelligence skill checks and Concentration checks. Requires an extra 2 hours of rest for a long rest.
- Bruised Hand. -1d4 to attacks made with offhand and two-handed weapons.
- Arrow to the Shoulder. Carry capacity reduced. Disadvantage on Strength checks to push, pull, or lift objects. Cannot use an offhand weapon or bow.
- Black Eye. That shiner is pretty noticeable. Disadvantage on perception checks and Charisma skill checks.
- Whiplash. Difficulty moving your head makes fine control difficult. Disadvantage on Dexterity skill checks, and -1d4 to attacks made with dex-based weapons.
- Gut shot. A strike to your gut makes it difficult to move your body with any agility. You can't apply Dexterity to your armor class.
- Cramps. Muscle overuse caused them to cramp up, and the pain is making you short-tempered. Disadvantage on Wisdom skill checks and Concentration checks.
And feel free to make up others appropriate to the attack that caused the injury.
No minor injury is permanent; it only affects things for the current day (or maybe the next day, if you get a second). It works on the same dramatic scale as HP. It's similar to the exhaustion mechanic, but less broad in the penalties, and no risk that it can directly kill you.
It's a way of saying that physical damage is actually a thing, but largely divorced from HP, because HP is not your real body. At the same time, it works on a daily scale, like HP does, and can be caused by things outside of combat.
Some minor injuries might not inconvenience certain characters at all, while others will be much more frustrating. The injury should be selected to be thematic, rather than specifically to hurt the character. If the barbarian gets his bell rung, he'll just power through it; he's not worried about intelligence skill checks. Same for a wizard that took an arrow to the shoulder. It's fine that the injury may not directly penalize them; it's more about the drama that they
kept fighting despite this setback, and that the flavor of the setback can be incorporated into play.
I would also consider this to provide the opportunity for more nuanced combat than simple "Victory or death!" It's a reasonable way to get an opponent to back off, similar to first blood duels, rather than simply run through all of an abstract number until the only available risk — death — shows up.
So those are my thoughts on how to deal with the HP abstraction.