In the DMG it suggests that the DM levels players at a rate of about 3 sessions per level past about level 5 or 6. My players' characters are currently level 8 and there are 7 of them. That would mean giving out about 4,750 XP per session to them. Since there are 7 PCs that would mean having them face 32K XP worth of enemies per session. I know 3 sessions is just the recommendation and not a rule, but I still want to move forward at a decent pace as party level goes higher. How can I do this without it being a major slog fest?
Larger monsters. The truth is, the XP equivalent number of kobolds would overwhelm a group faster than a group of ogres...or dragons. Unless, the group is made up of tanks that kobolds will never hit.
But, a large number of kobolds would be the slugfest you want to avoid.
Look at video games...Diablo and Skyrim. Both of them start with small monsters that are easy to beat. As the player skills up, the monsters become bigger. What they do, though is put in a mix of slugfest and boss monsters.
The variety is what keeps players involved.
Keep in mind that any society, whether a city-state or a dungeon level, has an order to it, with minions doing everyday labors, with an advisory group and a ruler.
So, one encounter, has a major slugfest, then have a group vs group, with near equal comparisons of skills (but within the XP target amount), then have the big boss fight.
If you find large combats that reward lots of experience points too much trouble, you can reward some of the XP for story actions that take less real-world time to complete. Reward experience for completing goals, rather than just for killing monsters. Bypassing a trap, rescuing a princess, negotiating a hostage release, and stealing a gem big enough to bowl with are all actions worthy of rewarding experience. You should be rewarding the same amount of XP whether the heroes kill the monsters, negotiate for passage, or sneak by the monsters. Not every hero's path needs to be strewn with the corpses of their enemies.
Alternatively, you can stop tracking XP, structure your adventures any way you like, and then simply level up all of the characters simultaneously once every three sessions. This is the "level advancement without XP" method of leveling up characters: when they accomplish something significant (that's worth about three sessions' worth of action), give them a level. Since players go through content at a semi-random rate (sometimes they take all evening to order a beer in the tavern, sometimes they blow through a session's worth of content in an hour), you'll end up either rewarding levels a little more randomly, periodically readjusting what a "significant action" means, or just deciding to give them a level once every three sessions anyway (called "session-based advancement").
Our group has rotating DMs with 4 separate campaigns, we can play about 3 times a month. As such, level advancement can be very slow. I wanted to tell a story that would allow the PCs to grow in stature without taking 5 years of real time to get through and which has significant non-combat action, so I simply doubled the suggested XP values. The result is that they still level about every three adventures without me resorting to padding the evening with XP-centric encounters.
The XP values are suggestions. If they don't model the progression level you like, adjust them until they are a good fit for the campaign you want to run.
Simply follow the DMG
Taking a look at page 82 in the DMG, a level 8 character has 2100 as the Deadly threshold and 1400 as Hard. Multiplying by the party size, you get 14900 for deadly and 9800 for Hard, per encounter. This gives you about three encounters per session (possibly including two deadly plus some RP encounters).
The 'Adventuring Day' xp table on page 84 gives an expected daily value of 6000 for level 8, meaning these ~3 encounters can (should!) happen between long rests. If your party is resting up their casters between every fight, you may not be pressuring them enough. Resource allocation is a very real problem for spellcasters.
On Slog Fests
I don't have a solid definition for 'slog fest', so I assume you mean a boring, rote kind of combat. Since the DM is responsible for creating combat encounters, if it's a slog fest it's literally the DM's fault. Fortunately, the DMG has several suggestions for making it more interesting, by which I mean harder. Taking a look at pages 82 to 85, here are some things that the DMG indicates make combat harder, with my indented notes:
- higher CR enemies
- Adult Silver/Copper Dragon
- Death Tyrant
- Monsters with class levels
- more enemies
- groups of Knights
- packs of Wolves
- packs of Blink Dogs
- varying types of enemies
- orcs backed by goblin archers
- cultists backed by priests
- summoned monsters and their summoner
- smaller party size
- try splitting them up; warning: don't over-use
- multi-phase encounters
- 'boss forms' a la video games
- surprise (ambushes)
- invisibility or camouflage
- environmental factors
- extreme winds (think desert sand-blasting)
- clouds of poison gas
- party mobility problems
- twisting corridors that break line of sight
- terrain preventing melee combat (cliffs, etc)
- party tied together for safety during mountain climbing
- field of boulders preventing effective use of reach to pin down enemies
XP is meant to be a guide. I suggest giving meaninful encounters instead of slogging through xp. But as a GM, you decide how to give xp and it doesn't have to be with 'monster xp.' You could set up some traps or a cool environment that the PCs must survive. That encouter with kobolds on a cliff face is surely worth more experience than the one with them out in the open. Be creative with encounters rather than slogging through them. Or give exp for totally different things like great role play, discovering new things about the world or the characters they're playing or even because everyone had a great time.
If you're running a combat-heavy game, it will be difficult to come up with challenging combat encounters for seven 8th-level PCs without it becoming a slog. The problem with throwing more monsters at them is that combat becomes complex. The problem with throwing larger monsters at them is that in turn-based games like D&D, the side with more attacks per round has a huge advantage. Big monsters either get to be so powerful as to be able to one-hit-kill individual PCs, or they'll be overwhelmed in a couple of turns by seven PCs.
Don't have a large party. D&D is really optimal for groups of 5 to 7 people, including the DM. ("Four or five players is best" -- 4e PHB, page 8.) See for example this Reddit thread on problems and solutions of running large groups. Commonly given advice for games with too many players is to split the game into two groups. An 8-person game like yours could play in two groups, each with 3 players and one DM.
Give out XP for non-combat encounters. For example, Matt Mercer has talked about techniques for running an XP-based game for a party of 8 tenth-level characters. Their game tends to run pretty well as it tends to be RP-heavy and combat-light.
Don't use XP. It's totally OK to just have the party level up when they complete campaign milestones. I even play in one game where characters level up after a fixed number of sessions, regardless of what we accomplish in those sessions.