[RPG] How to stress the players’ resources while making the stressors feel natural without simply adding more combat encounters

It sounds like you have two problems: (1) your game with 6-8 players has slow combats unless you use a small number of monsters, and (2) if you use a small number of monsters, your crowd-controllers can shut the encounter down.

The first problem is easier to fix:

• Use a larger number of monsters, but make most of them them identical so that you can run turns for them quickly. Move them all on the same initiative. "Okay, these three orcs are attacking you. Each of them makes one attack, with an attack bonus of +4... (rolls) they hit AC 11, 15, and 17. How many hits? Okay, take... (rolls) 12 damage." Optionally include one or two bigger monsters so that your crowd-controllers have something awesome to do.
• Consider splitting your game into two smaller games. You can start slowly -- have occasional "side missions" which don't involve the whole group. These will be easier to schedule: choose the time and place that work best for you, and see if around half of your players are able to be there. If that seems to work, you can have more and more side missions, and save the "full group" scenarios for boss fights and special occasions. In the extreme case, this turns into a West Marches scenario.

For the second problem: remember that D&D 5e is balanced around having a lot of encounters per day. Are you doing that? If you're only giving them one big fight in between rests, your characters with daily powers will be much more powerful than the designers intended, because they can use all their dailies in that encounter. Those crowd-control abilities: are they daily powers?

If you suddenly change your game from one fight per day to three or four, make sure to telegraph that in advance so your casters don't waste all their spells on the first fight.

One final note: it can be dangerous to have battles with a small number of active monsters. What tends to happen is each monster stands in one place and focuses all its damage on one player character. This is really bad for that player character, and it's sort of boring for all the other characters who never get attacked. One solution I've used for this problem is, when I have an encounter with just one monster, I make sure that all its attacks are area-effect attacks, so that it spreads out the damage more evenly. This involves a lot of inventing homebrew monsters, though, so it may not be best for every group.

0. Do your players want this, too?

If you haven't discussed a different playstyle I think they're reasonable to still expect the "sporty" style you were previously playing. That's why I think--even one session in--a change like this would be equivalent to starting a new campaign: same setting and same characters, but different game.

If you have not had that conversation, stop reading here. Talk to your players. If they agree on a new style, proceed:

1. Do it to them. Before you do it to them, tell them you're going to do it to them. And tell them while you're doing it.

"The hobgoblin captain has arrayed his shortbowmen on inaccessible ground and they're ducking behind full cover after each shot. Man, this is just a killing field! So, Gary, what do you do next?"

"OBJECTIVES, TERRAIN, COVER, VISIBILITY" are the four words I have written on my gm-facing side of my table tent. Use these to your advantage, and teach the players to use them to theirs.

2. Design your world, not your encounters.

Think about the people in your world, where they might exist, and what they value. Array them as makes sense in a world without your PCs. Do the encounter math as suggested by the DMG. Then don't modify anything!

Now you have a range of possible encounters including (a) not worth even acting out--just declare victory, (b) cake-walk, (c) very easy, (d) easy, (e) medium, (f) hard, (g) deadly, (h) superdeadly (would be deadly even at APL+1), (i) superduperdeadly (deadly at APL+2), (j) death sentence (could kill the party before they even act).

I'm not kidding: "no," "cake," "VE," "E," "M," "H," "D," "D+1," "D+2," and a frowny-face with two exes for eyes are notations next to possible encounters on the mind-map of my current adventure.

Now that you've got this in hand, you are prepared to properly describe the encounters as they happen. In a "cake" encounter your barbarian's axe cleaves enemies in twain (doing 9 dmg); the same hit in a D+1 encounter manages to annoy the enemy. But if you didn't do the homework, you're going to properly convey to the players the crucial information their characters would know: "we're in over our heads, here, and will be lucky to get out alive."

3. Help them find their way to spectacular victories.

There are many gm-styles and I'd naver say one is 'right' or 'wrong.' But if you're looking to help a group transition their style--or to learn a new style--I suggest that the one I call "find a way to 'yes'" may be really useful. In this approach you are explicit about asking players not only to describe their actions, but also their intentions. You work with them to craft their actions so that they to progress toward their objectives.

You don't have to pull any punches in combat or in their opponents' preparations and they don't always have to succeed. But this way their efforts aren't impotent even when unsuccessful. Failures aren't a matter of "the gm screwed us over," but are a matter of "the kobolds screwed us over." And successes can be spectacular. Like Hannibal says: "I love it when a plan comes together."