A few suggestions, apply those that sound fun to you:

1. Group creatures of the same type into a single initiative number. Or at least, put a good chunk of them to act on the same initiative.

2. Maybe don't act with all creatures. Some are probably stuck way on the back and do not get a piece of the action until the adventurers mow their way into them.

3. For each chunk of equal creatures, pick a group of targets, grab a handful of dice and roll their attacks all at once. Serves to drive up the point of their numbers.

4. Spend most of your time narrating during the player's turns, talking about their actions. Be less descriptive about mob attacks.

5. Add the mass of creatures to an encounter where something else needs to happen, not just kill them all. For example, the adventurers need to get to the other side of a large battlefield, not necessarily defeat everyone on their way there.

6. Enlist another player to keep track of the enemy hit points or the initiative rooster (maybe one for each). By splitting tasks, long battles are made shorter.

7. Make smaller minions die faster (give them less HP, instead of rolling dice or using the half + 1 suggestion, just use something smaller if they are disposable). Or make them retreat when weakened, which maybe allows adventurers to sneak in some opportunity attacks, ie. stuff to do while they wait for their turn.

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.