The short/long rest thing is also tied to expected encounters. The game assumes 2-3 combat encounters between rests and around 8 combat encounters a day.
So
Wake up
3 encounters
Short rest
2 encounters
Short rest
3 encounters
Long rest
Or something close to that, if you are not using that many encounters in a day than you might want to stretch the time out by changing what is a short rest and what is a long rest. If you make short rests an evening camping in the woods (8 hours) and a long rest a day spent in civilization (24 hours). It all works out if the encounter structure is something like this.
Monday morning leave town.
Get into a random encounter, and one planned encounter.
Monday night (short rest)
Tuesday get into 3 encounters while exploring an old tomb.
Tuesday night (short rest)
Travel for 3 days getting no real quality sleep because of horrible weather. During this time get into another 3 encounters.
Make it to a new town and spend a day shopping and sleeping in a good inn (Long Rest)
You still have 2-3 encounters between each rest, you still get 8 encounters before a long rest. Resource management mostly stays the same. There are long duration spells like hex and hunters mark that get reduced in effectiveness but you could change those up if it becomes an issue.
This way a nights sleep is like a short rest, ie allows you to spend hit dice.
For hex crawling where 1 encounter a day is normal, and other wilderness exploration games this works well. Not so well in a long dungeon crawl which the base system is designed for where you do get into 8 fights or so in an adventuring day, to it depends on the type of campaign you run.
The real solution is to leave rest frequency / duration up to the individual scenario.
It is the idea that all rests must always work the same that is the problem.
Most groups enjoy variety in their adventuring, doing a dungeon one day and trekking across the wilderness the other month.
So instead of saying three encounters, rest one hour, three more encounters and then sleep for the night;
Instead say three encounters, short rest, three more encounters, then a long rest.
You're so very near, then you (as does everybody else) start talking about changing short and long rests to day/week...
With long and elaborate examples. All for nothing. As if that's gonna solve anything. Perhaps you solve the wilderness trek, but instead you break the dungeon.
The truth is that no given value for a rest will work for all or even most adventures (unless all you do is dungeon bashing!), so why bother?
Why not settle for the basic fundamentals: three encounters, short rest, three encounters, short rest, three encounters, long rest...
...and then give general advice that works in all cases? "in dungeons, a short rest taking as little as five minutes could work; during extended and relatively eventless voyages, a long rest per port of call or oasis could be appropriate even if separated by weeks"
And so on.
Man, I wish this stuff was in the DMG.