That's sort of what I'm doing right now.I've long sense made short rests way shorter even without using that concept. Like 10 minutes. It's just easier to handle in play.
Also if you wanted it to be more flexible in when you take your short rest, just add an ability of "Take a short rest as a single action, this ability refreshes on a long rest" to all characters.
Long rests = 36 hours in a safe location.
Short rest = overnight
But once per long rest a short rest can be taken for free.
(This last one gives me and the party a bit more freedom to vary the daily structure of encounters.)