Hmm. I certainly sympathise with your goals, but I can only find tweaks that make the game more deadly and slows down recuperation.
Would this not just shift the general difficulty of the game upwards?
My own theory is that deadly encounters are fine, it's easy encounters that need to become more challenging, and not because they get individually harder, but because the resting pace is changed to fit each adventure.
In a hectic dungeon bash you might want allow 5 minute short rests and 1 hour long rests.
In a epic ocean voyage 1 day short rests and no automatic long rests at all (only when the ship is in port) might work better.
In the end, it boils down to one fact and one question:
Fact: the easy encounters need to come in clusters (up to 6-8) with no long rest in-between to be mechanically relevant.
Question: do you want the players to be able to influence the number of long rests, and hence cut down on the number of encounters between each long rest, even when that destroys any semblance of challenge?
(The default answer is an unreserved "yes", since the PHB is shock full of spells and other resources that allow the party to take long rests pretty much anywhere.
The opposite is a simple no, as is the case when you run with the Tweet rule where you need to have two encounters before you can benefit from a short rest, and you need to have two short rests before you can benefit from a long rest.
The advantage of this system is that suddenly all kinds of adventures work automatically - from the hectic dungeon bash mentioned earlier to the epic ocean voyage.)
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