I ended up creating my own healing/HP recovery system for my last campaign, trying to balance a decreased HD expenditure/recovery mechanic. It didn't work particularly well, primarily because it wasn't intuitive or easy to remember - trying to balance rests and HD recovery, Healer Feat, Healing Kits, etc.
We tend to play a more "old school" style and pacing, where you're not having 6-8 encounters per day unless you're deep into the end game of a particular adventure, and even then, the recovery/rest/prep for the major encounter is pretty much a given. So my players always expected to be able to rest in a dungeon (we have done this for 40 years

, and/or prep before the final encounter. They definitely don't take to going in against the bad guy without being near peak (regardless of ticking clocks, etc.). 5e makes this even easier with Leomund's Hut, etc. So unless I specifically tailored the enemies against this, they could rest wherever in perfect safety.
We changed all of our short rest abilities to PB times/long rest to smooth out the game, and allowed up to 2 "short rests" which allowed HP recovery "whenever". Wasn't great either.
With our pacing, the Gritty Realism may have been better, but you can bet that every one of my players, except the fighter types, would have switched to "short rest" recharge characters, rather than anyone with a long rest under that system. That's just the way they game the system.
So ideally any HP recovery system is 1) simple, and 2) can support varied pacing of the game. HPs should take longer to recover, and fighting shouldn't be the default game state.
We're switching to Basic/Expert for our next game. I'm already frightened, and all I've done is roll up a character.