I feel like the most elegant way to get to a 3-4 encounter/day paradigm with "widely applicable rules" is this:
1.) reduce the amount of time that short rests take--5/10/15 minutes, whatever feels right to you.
2.) give PCs a "long rest pool" of short rest feature uses equal to 2x their normal # of uses of each feature.
3.) when PCs take a short rest and recover their short rest features, they deplete their long rest pool.
It's the equivalent of allowing two 5-minute short rests per day, but with less cognitive dissonance.
example:
Branwen the 4th level battlemaster has 3 short rest features: second wind, action surge, and 4 superiority dice.
Her long rest pool at the beginning an adventuring day is 2 second winds, 2 action surges, and 8 superiority dice.
If, on the first encounter of the day, she uses action surge and 3 of 4 superiority dice, she can catch her breath for 5/10/15 minutes and get those features back.
Her long rest pool after the encounter will be 2 second winds, 1 action surge, and 5 superiority dice.
edit: yikes, it looks like
@FrogReaver suggested this first