[RPG] use the Monster Stats in the DMG to estimate a party’s damage output

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.

All D20, but DnD 5 especially, are designed and balanced assuming a 4 or 5 player party. And you can kinda tell, when the rules start asking you to apply multipliers to bigger parties, rather than giving any concrete guidelines. Assuming distributed player competence, a 6 person party isn't simply 20% stronger than a 5 player party. It's much higher. There's an entire additional PC, with their own suite of abilities, magic items, and most importantly, actions. Never underestimate the power of having more standard actions than the other guys (unless you're a pack of CR1/2 minions going up against a bunch of level 5 adventures, then you're screwed either way).

In short, designing challenging encounters for big parties is one of the more substantial challenges a GM may have to face. There seems to be a razor thin design space between "no actual danger" and "guaranteed TPK" when planning for large parties. My own personal strategy is "5 players per party max unless you have a super good reason that a sixth needs to be in this particular game, and never ever ever ever more than that (and preferably not 6 for long)," but that probably won't help you, specifically.

First of all, stop giving them one big thing to focus on. There are a couple iconic encounters that tend to necessitate one big monster against a party of intrepid heroes, like dragon slaying. The problem here with big parties is 1 creature generally can only attack one thing at a time, so even if the beastie is downing 1 PC a round, the rest of the party can pop cool downs and beat the timer. If you design the combat space so the beastie can use it's AOE abilites to good effect, you often find yourself looking at a TPK. Quantity may be a quality all it's own, but it isn't everything. Basically, when the party is that big, the single monster encounter HAS to be able to one round KO any given PC, or it's not a threat. And while it's killing one PC a round, the remaining party members HAVE to have a DPR high enough to whittle the beastie down before it kills them all, or they all just die. SO! Anytime you're tempted to let 7 or 8 dungeon crawlers dogpile one big boss monster, resist the urge. Instead of fighting one wyrm, why not a mated pair of adults, maybe with a wyrmling thrown in to harass the squishies? (Actually, this particular piece of design advice sort of holds true for any size party if there's more than one healer to keep the front liners standing)

Secondly (related to the first), if your party outnumbers the monsters, they'll probably win unless each monster is SIGNIFICANTLY stronger than the PC. I can't give concrete CR equivalencies because it's different at different power bands, but 7 lvl 5 PCs who know which end of a longsword is pointy should mop the floor with 5 CR7-8 monsters. The power of two players worth of extra actions is too substantial to ignore. Design the encounter using the guidelines in the DMG, then add a few support casters or bowmen(or bowwomen, or bowgoblins, or bowwhatevers) at a little under CR to bring the numbers within 1 of the party.

Finally, if you're going to do mob (mob in this context being a large angry group, not a MMO enemy, nor a crime family) encounters, consider looking at the minion style monsters from 4th edition. They had decent defenses and attack bonuses, but 1 HP and very low damage. Custom brew up something mob-able, maybe give them advantage for being adjacent to allies, with a decent attack bonus and a beefy AC, but a damage range of a d3 and very low health. And remember, mob fights aren't typically meant to be challenging in and of themselves, they should be hard enough to drain some resources while letting the players feel like badasses for steamrolling through a pile of enemies. Remember, damage spread to 7 players hurts a party much worse than that damage stacked on 1 or 2 frontliners.