Have you tried just making the combats more difficult?
There are two parts to the encounter quota. First is attrition, and yes by making encounters more deadly you can deal with it.
The second is inter-class balance between the at-will classes like rogue (or EB-only Warlock) and the long rest recovery classes (like casters) and to some extents hybrids (like paladin or barbarian). I don't think anyone will say that a single average martial round will do as much as a single average round of high level spell casting. High level limited resources > at-will ability. True and good. If there is a single round of combat in a day, we can see how the casters will be able to accomplish more than the at-will characters. By the flip side of the same coin, if long rest only happened once per level the asters would be predominantly cantrips for the level, and at-will class action > cantrips.
So the real balance point is somewhere between - where the efficiency of high level slots and the lows of cantrips and balance out to the same average per action as what the at-will classes dish out. Having fewer, tougher combats that wipe the casters out of high level slots isn't enough - they still have a higher efficiency per action. You need to have them take a good number of cantrips or other actions that as less than at-will primary classes to get their effectiveness per action to reduce and equalize.
And it's even more complex than that because a lot of long-rest-recovery resources will last for longer than an average combat, so they are actually more effective when you run fewer combats. A buff that costs a single action and single slot that lasts for 3 rounds is and the same cost but lasting for 8 because it's a longer combat isn't reducing the effectiveness per action, it's increasing it. An easy way to think is a low level barbarian - what's more powerful, a barbarian that is raging every combat or one that's raging half the combats.
And this doesn't even consider short rest primary classes like monks, because short rests can be handled in different ways by DMs as well.
To sum up: outside of deadliness, the encounter quota helps balance out the difference recovery model classes with each other.
Addendum:
This isn't me pushing the encounter quota system. I dislike that it's needed and I can't just do whatever pacing the narrative delivers, and where it's calibrated is the single biggest weakness in 5e for me because it's at a place that no one goes regularly except possibly during a dungeon crawl. Definitely it isn't exceeded as frequently as it's short. I wish the design was quite different and it wasn't part of the game at all.