[5e] Rest Mechanic Variant Homebrew

Hey all. So I'm running some groups through LMoP at the moment and thinking up our next campaign. I've been playing for a bit and DMing and one thing that gets to me is the gamey feeling of things. Hacked limbs heal in hours, heroes reset abilities almost like a cooldown, and overall players simply become way too strong way too fast. I like a harsh, gritty, realistic world where players think twice about battling that troll or demon and from talks so, too, do my players. Likewise, I've been trying to come up with some variations to increase the grit and danger while keeping things fun. I'm also interested in making off-character types more fun to play.

With that said, I'd like to share my working idea on changes to the rest mechanics. I'm looking for constructive feedback. I'm not completely satisfied with what I've come up with, but I also like where I'm going. Who knows, maybe I am done and I have a good system. Think of these as taking place in a OotA, CoS or some other non-time-sensitive setting.

Short rests:

4 hour short rest functions as vanilla

Optional 1 hour short rest - Characters spend a use of a healer's kit and pass a Medicine DC10 to give themselves or another player 1 hit die. This action can not be repeated during this rest. Players may not receive more than one of their hit die during a one hour rest.

Long rest:

Long rest base is 1 day. This does not heal you, however.

Players can add an additional day of rest to gain healing via hit dice. Each day of healing adds a set of dice equal to their tier level. For example, each day would give a tier one character +1 hit die while a tier four character would get +4 hit dice.

These hit dice do not come from the normal hit dice allocation. They are, in essence, "free". The type of hit dice is still determined by class and remains the same as a character's normal hit dice type.

Any player may pass a Medicine DC10 check to give another character +(tier bonus) worth of hit dice. This action may be repeated once per resting day. Expending a healer's kit (not one use of one, it spends the whole kit) for this action gives advantage to the roll.

The amount of days resting must be declared ahead of time. This simulates the preparations taken to prepare for the rest and the continuation of adventuring. If players wish to add to the agreed upon time of rest, they must spend an additional day as in the long rest rules.

Any players wishing to attempt healing must also designate which days they will attempt the healing ahead of time. Think of the time that a long rest begins as set in stone.

(for anyone wondering, this is to encourage slightly longer rests than may be needed. I think the two weeks the DMG suggests is a bit much, but 4-5 days sounds good)

Any healers kits used to attempt healing is used regardless of results.