This is certainly a possibility, but one of the things I missed about AD&D was the long stretches of recovery time. This gives the dungeon denizens time to prepare new traps and ambushes. Is the party tearing through encounters with tactic A? Well, the goblins have had 10 days to come up with counter-tactic B.
Arent the PCs in the dungeon to rescue someone? There was some 'magic fruit appears on day X' thing as well from memory. Im sure you could easily insert one of many time pressures to keep the PCs from resorting to the 5 minute adventuring day.
From memory the NPCS the PCs are sent in to rescue are already dead (and tree zombies) but that alone should be enough to keep them pushing in as long as they can, and not relying on the 5 minute adventuring day.
Slow Natural Recovery didn't have as big of an impact as I was expecting. It's definitely a lot funner than the default rules, but you can still expect the party to be at full or nearly-full health after a long rest. Yes, the party will be resting a little more frequently, but it's not like AD&D where they had to hole up for several days at a time.
I use:
Short rest (5 minutes): Allows expenditure of (1/2 level, round up) Hit dice to heal. Roll one at a time, adding Con to each die till you're happy. Restores all short rest abilities. Generally limited to a maximum of 2/ long rest (in special or unusual circumstances the DM might allow more).
Long rest (8 hours): Restores no HP. First you recover 1/2 your level in Hit Dice (round up). Then you can spend 1 or more Hit dice immediately if desired. It also restores all long rest resources to full, with the exception of spell slots and Warlock arcanum. Spell slots recharge at the rate of 1 each of levels 1-5 for each level you have slots available, plus one of levels 6+ (or one arcanum) if you have spell slots of that level. You can choose to restore a lower level slot in the place of a higher level one as long as you have access to slots of that level. Limited to 1/ every 24 hours. If interrupted it only counts as a short rest as as long as you havent had more than two short rests in the past 24 hours, forcing you to start again.
Example:
Harry the 9th level Wizard can short rest twice, for 5 minutes each time, expending a maximum of 5 Hit dice on each rest (to a total of 9 HD during the day). When he long rests for 8 hours, he first recovers 5 Hit dice, and can spend up to 9 Hit dice (if available) if he is still injured to heal.
He also recovers 5 spell slots; 1 x 1st, 2nd, 3rd, 4th and 1 x 5th level slot.
I find this keeps day time pacing where I want it (no immersion breaking 1 hour stops in the dungeon), is punitive enough with slot recovery to keep casters from nova striking encounters or constantly seeking to drop high level slots into every problem, and keeps healing fast enough to keep the adventure going without week long breaks in the action, but slow enough to make hit point attrition a thing, and a two or three day adventure requiring 3-4 days for everyone to get back to (full HP, HD and spell slots).
I also use negative HP, and death at (-10 or 1/4 max HP, whichever is better for the character). Its a DC 15 Con check to stabilize (Champion remarkable athlete helps for this yay!).
Each check you fail you lose 1 HP. Each check you pass you remain on the same (negative) HP total. If you fail 3 you gain a level of exhaustion. If you pass three you're stable. Once stable, you come to in 1d4 hours with 1 hit point.
That said, there's no perfect way to remove Hit Dice from the game without introducing new problems. For example, the fighter (with Second Wind) will laugh at your attempts to reduce his healing capabilities. Sure, you can make Second Wind a once-a-day ability, but I have a strong aversion to house-rules. Slow Natural Recovery has the benefit of being an official variant, and it doesn't introduce new problems, so I like it.
Limit short rests. The game isnt intended for the players to take multiple short rests in a row, doing nothing else. Literally; just say 'you sit around for an hour but you're already as rested as you could possibly be from the short rest you had immediately prior. Your abilities remain expended till you take a long rest'
The party has a Ranger with 14 passive Perception. They are walking toward a pit trap. The adventure text says: "It takes a successful DC 15 Wisdom (Perception) check to detect the trapdoor's presence."
You, the DM, roll a 1d20. Take the original DC, subtract 9 from it (15 - 9 = 6), and add the result to the d20 roll (1d20 + 6). This is the trapdoor's new DC.
I like this. A lot. Consider it stolen.