The typical inter party balance is because of the single encounter day due to narrative reasons.
Multi encounter days end up being few and far between, so short rest classes suck.
This is a narrative pacing problem. Just switch to "gritty rests" with an overnight sleep being a short rest, and a week long "nothing to do" downtime "vacation" is a long rest. Now your long rest classes will husband their resources jealously.
This probably matches the pacing of the adventures of most people with 5 minute adventuring day issues. Just make sure that "taking a week of downtime" is a "story level surrender", and arrange for such downtime between stories (ie, if story X unlocks Y, ensure there is a week of travel or something in between and not "it must be handled ASAP")
It means your "big boss" fights can't be as tough. And the multi-encounter day gets balanced for "between short rests" not "between long rests", so again not as tough. But that is completely within the DM's control.
If you have "epics", like require more than 1 big boss fight, start the bad guys doing things on a roughly weekly basis if not stopped (roll 4d4 if you want).
Ie, suppose you have an epic that needs about 4 full "adventuring days" worth of encounters in it. Lay out this timeline:
Code:
[INITIAL BAD GUY THING, KICKS OFF EPIC]
[BAD GUY DOES ANOTHER THING] (4d4 days after initial event).
[BAD GUY DOES ANOTHER THING] (3d4 days after last event).
[BAD GUY DOES ANOTHER THING] (4d4 days after last event).
where the players actions can quite reasonably interfere with the bad guy plans. This can slow down the steps, make bad things not happen, etc. The "story" consequences should be up front; the bad thing isn't "PCs are ambushed and killed or attacked", but rather "zombies attack the warf" or "king is assassinated".
For each of those bad guy things, you can split it into tiers -- "thwarted" and "unthwarted", where the first is what happens if the PCs won the last "story" piece of the epic, and the second if they fail it (possibly because they wanted a nap and took a week off).
You can even explain to the Players (not the PCs) that the bad guys have a calendar, and you can take vacations, but when you do, the bad guys plot advances in the background. And that some vacations are going to be assumed. Just don't take them needlessly.
In each of those pieces, stuff in some encounters. An adventuring day each or so.