I've had a house rule for hit point advancement bouncing around my head for a while that might help.
Characters only gain 1+Con mod HP per level (minimum of 1). Characters still have the normal amount of hit dice available to use during short rests.
Bounded accuracy means low level monsters can still hit PCs but hit point inflation means the damage becomes pretty negligible at higher levels. I'm hoping(Haven't actually tried it in play yet) that this rule addresses a few issues:
1) shortening combats by reducing the HP grind at high levels
2) make smaller encounters more deadly. At level 11 it takes 24 orcs to make a hard encounter for a party of 4 PCs which slows things down a ton
3) still let PCs handle more encounters before resting as they level up. Keeping the number hit dice the same means it's easier to get back to full health and keep going so there's less incentive to take a long rest.
Not sure if that helps but I wanted a way to extend the feeling that the lower levels have, where any one encounter can turn deadly and things like orcs and humans are a major threat, while still letting the PCs have the fun of leveling rather than stopping at a certain point. I also think this rule could pair well with the longer healing variant from the DMG if you wanted to slow down spell casters and other rest based abilities
Someone posted a pretty fantastic work in progress hack to HP and Hit dice in the homebrew forum a while back.
Basically everyone gets static, low, HP, and then hit dice are an active resource that you can choose to spend when hit to reduce the incoming damage.
It's very extreme, but it looked like a cool mod that might evoke the feel of E6/Savage Worlds/etc.