Potential name: The Physarum Harem. (Checkout that link for awesome slime mold action. Too hot for TV!)
Visually the entire dungeon I imagine being an internal perspective of that.
Before the bulk content, I think a fun, different mechanic for this dungeon would be that it's spawnable (Rare, calm down). Slimes are already known for this and piss miners off like that, and I want to keep that feel. Of course it would spawn with a stupid amount of slimes, don't worry! Of course some of those slimes might be the special nasty variants found inside! Of course the dungeon entrance itself might act as a slime spawner for more of these nightmares, rendering that portion of your mine unusable until the problem is dealt with! Sherlock, this game is meant to hurt.
Room Landscape Features:
So far we have water features in Beaver Lodges and cliffs in Bat Roosts, so the slime pits need their own unique topographical... thing.
Slime pit rooms could be extremely large and open, but with solid gelatinous tiles forming a secondary structure that makes the rooms much more convoluted. The fairly randomized result is that you might need to mine/bash your way through some of these tiles, which have a much higher chance of spawning slimes. Slimes could move through these tiles unhindered. This could result in messy situations where the room generates quite a zig-zag pattern of slime walls that you need to flee back through. Mining/bashing these tiles could result in reverse-caveins, where destroying one tile could result in nearby tiles also being destroyed, potentially releasing trapped slimes.
I imagine people retreating from a rough room, through a zig-zag corridor that they themselves may have dug, only for slimes to path straight through the winding route, disappearing at one wall and reappearing on the other side.
Leaving the slime pits for a prolonged period of time could result in the gelatinous tiles rearranging, undoing any progress made.
Inhabitants:
Flux Slime: Not a direct enemy, but a particularly fluidic and motile wall tile that shifts regularly, even onto inhabited tiles, and results in slowed movement like in shallow water. Slimes are not affected. Not sure about the feasibility of this feature currently, might not be very easy to implement at all. Visually a big ol' rectangle of slime. OH! Maybe they have a bias in their pathing and prefer to clump around players? Yes, that. Not strong enough to pummel prey to death themselves, instead they restrict player movement and allow other colony members to finish them off. We need David Attenborough.
Generic other colors of slimes: Dungeons need a nice variety of enemies, even meatshields, so I like the tradition of different colors of slimes here. Cue picture of the slimes from a game I'm partial to:

Source: Sword of Vermillion
Maybe a slime variant that is especially corrosive to armor. Another that has a nasty unique infection that causes severe slowness. (That's a theme here.)
Slime splitting is something I guess you could vary among them, like having some types be more prone to splitting, but that feature has always been more frustrating than engaging.
Slime SPITTING on the other hand, could result in a nice new ranged enemy. Giant Gray Ooze, really slow, shooting you and each shot spawns lesser enemies. Definitely shouldn't be an infinite ability, in fact if possible they should reduce in size and damage proportional to the amount of slimes they've spawned. Ugh, regular slimes should do this. Maybe have dungeon features where this type of slime can "recharge" (Jelly Fountain) and regain mass. Harvestable for "Protoplasm."
Boss: The Nucleus: surprise, you actually end up fighting the dungeon itself, bit of a trope but applicable. And yeah I know slime molds and fungi networks are multi nucleate irl, please reinvest in some suspension of disbelief for effect. Fuck it call the doors dolipores. The nucleus is fairly weak, but with absurd HHP and opening reduction moves. The danger is from the mountain of slimes, oozes, and other assorted jellies that swarm from the walls to protect it. Lets face it, slimes in H&H are famous among us for the swarm situations, and what better boss that a continually spawning swarm of these new and varied jerks, along with needing to lay a beating down on the boss itself? This almost demands a team effort. People using AoE combat moves and others trying to focus on the boss while fighting back the literal tide of enemies. (Striking the nucleus should probably spawn some and attract a percentage of already spawned nearby ones.)
Spoils of War:
Just as the theme of the dungeon was being miserable to miners when spawning, its rewards should be wonderful to them. Firstly, and I don't know why this is so important to me, but it seems like every slime variant should have its own unique slime corpse item. Maybe make "slime" a category that these all satisfy. Metallic ooze that you can smelt and acts like a weird combo of all gold and silvers. Flux ooze that drops random items from previous prey (Pulled from the global fishing pool). Blue jelly that grants EXP. Purple glop that cures that rash you've had for a bit but don't have the health insurance to get it looked at, and other mining diseases. Red ichor that acts as long term tar fuel for lanterns and torches. Generic dungeon cytoplasm for num nums. Dungeon boss rewards I'll leave up to the devs.
Edit: Spoilers removed, I thought they'd cause the selected text to be in a collapsed box, not that weird negative highlighting.