This natural healing results in much faster recovery than the standard Gritty rules, and makes a cleric or paladin an infinitely better tank than a fighter or barbarian (adding a cleric or paladin adds much more to the damage your party can survive per day than a fighter or barbarian does in almost all circumstances).
In practice, adding an extra cleric (or anyone with decent healing magic really) would make almost all of these additional rules mostly noise, if your cleric was willing to spend resources on healing (or had such resources to spare).
A more direct criticism of mechanics presented:
Your "modifying hd rolls" rules is full of quirky mechanics. "up to skill modifier", "roll twice", "proficiency bonus targets", "increase DC by 2 for each extra target" are used, each one with a different mechanic, for what appears to be no good reason.
Ability score drain isn't impacted by your resting conditions.
You state "DC 13 Constitution", but do not state it if it a saving throw or ability check (or, I suppose, attack roll, heh).
Shelter rules exist, then Sleep mentions Shelter again.
There are a lot of rolls you are making every night. Let's see.
1. You need to find out how many people want to spend HD, and order them by importance.
2. If you have someone with good survival, they roll to provide shelter for the most important. This probably covers everyone unless the party is large. Then weaker people start rolling, so long as they have a positive bonus. (PCs with +0 survival are unable to ever produce shelter it looks like, and negative bonus PCs remove shelter if they try). Advantage from unskilled helpers is likely.
3. Food is unlikely to show up, unless the party runs out of rations. Even then, the impact is going to be relatively small; running out of food is going to be a bigger problem before dropping HD by 1 size is.
4. Sleep you can't do until you check shelter or there is an ambush. Now you do your DC 15 Con(survival) checks (off-attribute skill use) if needed.
5. Finally, you'll do medicine checks. You'll reevaluate how many people need significant healing and decide how many get care.
Problem: There isn't going to be much story generated here, and there is going to be a lot of relatively fiddly mechanics. Failure results in "you heal, just a bit slower".
... For players, I suspect the result will be attempting to engage with these rules as little as they can.
For DMs, I'd have to have them printed out and consult them at each stage I suspect to not get them wrong.
...
It could be cleaned up. Tidy up the requirements.
The survival days thing might be worth looking at.