No, this does not exist in 5e.
Implementing it in 5e may be less satisfying, since the increase in proficiency bonus covers many of the incremental advancement options from previous rulesets in one swoop.
So for the fighter, for example, you'd have two options - the one feature they get every level or the proficiency advance they get every 5th level. It's pretty difficult to make that incremental. Even with something like a druid, they get a spell advance and then 0-2 other improvements. Within a single level there's not enough advance, on average, to break it up much.
Another way to implement incremental advancement is to let the character apply the next larger proficiency bonus to one of (attacks, saves, skill checks) per level they go up (not between levels). That seems pretty fiddly, though, and lets someone min-max what they're already good at levels ahead of time.
There's no hard-and-fast set of rules on this. But we've got a few touchstones that can inform a good scheme:
1. PHB: skilled laborer. Skilled laborers hire out at 2gp per day. But do not equate the work of even a level 1 adventurer with that of a skilled laborer. The unskilled laborer is told: carry those bricks. The skilled laborer is told: build that brick wall. The adventurer is told: there's a set of ruins a few miles away, possibly infested by who-knows-what, but we really want the bricks from there.
The danger faced by the adventurer makes their labor rate significantly higher than that of an equivalently-skilled mundane laborer.
Labor rate: >2gp per day.
2. Adventurers League: spellcasting services. In evaluating how much an adventurer should be paid, we can assume that spellcasters may be required to cast their spells, and all AL modules contain a table of costs for spellcasting services. Level 1 spells cost 10-20gp, and your level 1 spellcaster might be called upon to cast 4 first-level spells in an adventuring day (assuming a pair of short rests).
Spellcasting rate: 30-80gp per day.
3. The Castle Guide: "Heroic Services." The Dungeon Master's Guide (5e) lists the construction+labor costs of various strongholds on p.128. Some months ago I ran each of those through the cost-estimating scheme in 2e's DMGR2: The Castle Guide;1 I can assure you that the 5e and the 2e economies track very nicely.
The Castle Guide tells us that a PC should be counted as worth an extra person's labor per character level. In addition, spellcasting PCs should be additionally "credited" a man-day of labor for each level of spell available. Thus a 4th-level (5e) Wizard should be worth the labor of 1 + 4 + (4x1 + 3x2) = 15 skilled laborers, while a 4th-level (5e) Rogue should be worth the labor of 1 + 4 = 5 skilled laborers.
Your characters, at first level, are then worth between 2x and 4x more than a skilled laborer.
Heroic rate: 2x - 4x skilled labor
Putting it all together:
Taking all of this into consideration, a "first-level adventurer's rate" of a few dozen gp per person per day is reasonable, and that should scale pretty quickly with level.(Say, 30 gp/adventurer-day at 1st, 60 at second, 90 at third, &c.)
1 - A player wanted to rebuild a certain Keep in Princes of the Apocalypse after some... devastation. Introducing him to The Castle Guide--after exhaustively vetting its numbers against 5e touchstones--provided him many hours' fun away from the table.
Best Answer
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.