Grittier resting rules? Like, you want resting itself to be a struggle? Just start off each PC at the equivalent of 50 years of age. Sleeping gets grittier around that time for most of us.
If you want resting to be less effective and more 'realistic':
Use short (1 hour), long (1 night), and full (1 week) rests. Spells and abilities recharge as normal during a short and long rest. Healing works differently.
During a short rest you may use a a healing surge. Roll hp to recover as normal when using healing surges, but any value from the surges in excess of your hp loss is ignored. However, you split up the hp recovery into three buckets: 25% (rounded down) that you get back from the short rest, 25% (rounded down) that you get back at the next long rest, and the remainder which you will roll to recover during a full rest.
You only actually get back 1/4 of the hp when you short rest (rounded down) with the remained reserved to be regained in long and full rests. You'll get back another 1/4 the next time you long rest (rounded down) which may mean you're gaining back 'another quarter' of hps from several short rests during the same long rest. After each full rest (which requires you to be not doing anything strenuous for an entire week), roll (2d4 -1d6+ constitution bonus) (max 10). Multiply that by 10% rounded away from zero. That is the percentage of the 'remaining' hps you get back (or potentially lose) after that week.
Example: Bob is 5th level and has 40 hps. He takes 21 hps. When he short rests, he uses 3 surges and gets a total of 24. As 24 is 3 greater than 21, 3 of those are ignored and we focus on the 21. He gets back 1/4 (rounded down) of those 21 (5) after the short rest and 16 are yet to be recovered. He is at 24 hp, now. He takes 12 more and short rests and uses his last 2 surges - rolling 20! 8 are again wasted. He can't apply them to the hps that were allocated to long and full rests before. So he regains 3 (25% of 12) now and reserves 9 more. When he long rests, he has 15 hps and has 25 in reserve. He gets back another 5 from the first short rest and another 3 from the second short rest (8 total) which brings him back to 23. He has 11 hps from the first short rest and 6 from the second he has yet to recover (total 17). He recovers his 5 healing surges and could use them if wounded again, but the adventure ends and he returns to town and spends a quiet week recovering. At the end of a week he rolls the dice. On the 2d4 he gets two 1s. On the d6 he gets a 6. His con bonus is 2. 1 + 1 - 6 + 2 = -2. We multiply that by 10% and get -20%. He multiples the 17 down he is by -20% and gets -3.4, which we round away from zero to -4. He loses 4 hps. meaning he is now at 19 of 40 hps. At the end of the next week he will roll again and multiply the percentage againts the 21 hp down that he is at.
If you want to use more gritty rules, you can apply modifiers to the 2d4-d6+con roll for certain wounds, medical attention, poor conditions, etc...
My side recommendation for grittier everything is: Run episodic adventures so that you can sub out PCs that get ruined. Don't try to run a megadungeon when the PCs are going to be falling apart and need months to recover.