So for days where combat is the primary encounters, you guys typically (but not always) have a combat after a long rest, take a short rest, have a combat after the short rest, and have a long rest?
We get in rests whenever the story warrants it.
If the PCs are in a place of relative safety and can get in a short rest, they will as long as it makes sense and a couple resources need replenishing.
A long rest only occurs if the PCs are in a place of safety, fortification, etc. Often times this is when the rest for the night, but after taking out pretty much all threats in an adventure, a long rest before the next journey makes sense--and the location is "now a place of safety" due to the removal of all threats.
That’s the thing, if you had 8 combat encounters per adventuring day, in the real world a day would last months!
So what? As long as you are completing the story/adventure, what does that matter?
The story should dictate how many encounters happen during a day "in game time", not some artifcially forced mechanic. If it takes you a session to finish three combats how does that really impact things for you?
Suppose an adventure has 11 encounters, such as infiltrating a bandit camp or something. You have scouting, patrols, etc. and then moving into the camp and taking things out looking for captives, etc. The PCs have been traveling during the day to get to the camp (maybe a few random encounters depending on the travel distance), then knowing time is a factor have one night to accomplish their mission.
They might get in a short rest when they arrive, but they can't use 8 hours for a long rest or over half the night will be gone! So they start scouting out the place, and then formulate a plan, and move in. If you have a few buildings, with a couple rooms or more in each building, you can easily have 10 or more encounters. But you have to get through them all in that one "game night", so it will take you 3-4 sessions or more.
Here is a map I used for such an adventure and I've numbered the place where encounters happened. There was basically about 20 encounters (including outside patrols, etc.) not to mention the 3 or 4 encounters to get to the stronghold. It took us 6 sessions to complete everything (1 to get the adventure, travel there, and scout, 2-4 clearing out upper level, 5-6 clearing lower level). The PCs got a short rest after arriving, and another short rest after clearing out the upper level. They didn't get a long rest until they finished session 6.
Now, not every adventure is like this of course. And we do play mostly every week, which I know is getting rarer and rarer IME for most groups.
Otherwise, IMO it would feel artificial and like a series of one-shots if you try to keep a long rest / end of day when you end each session.
Could you outline what a typical session for you looks like? Maybe it wouldn't feel as bad as I imagine it would for me...?
Come to think of it, the heroic variant (5 min short rests, 1 hour long rests) might appeal to groups who like ending the session on a long rest?