playing them 'above board' sucked the life out of them by turning them into a series of dice rolls and spoiled invest in the narrative.
Reducing anything to a series of rolls instead of a series of actions, resolutions, & descriptions is going to suck the life out of it, yeah. It's why combats can so easily go from fast to boring, and why diplomancers were such a pain in 3e.
I agree, but that doesn't mean you can't steal the mechanics. Set up obstacles then describe them as the PCs would see them. So the shaky bridge, the collapsing ceiling, the door that is stuck closed while the room floods ... all part of a skill challenge described from the perspective of the PCS while the DM takes note on their score.
There was actually quite a bit to SC. It's easy enough to lift
n success before 3 failures. Just let players declare actions and call for checks until either three have failed or enough have succeeded. It's a little arbitrary and disjointed compared to just setting up the situation and playing through it in detail, and it really requires you to abdicate 2/3rds of the resolution process by always calling for a check, but you can do it.
I'm just not sure there's anything to be gained by it. Skill Challenges were much like encounter design guidelines & combat rules (just a whole lot less to them than the latter), they gave you a gauge of difficulty and a structure for resolution. The former was a major part of the appeal, you got guidelines for difficulty, depth, and exp awards - very paint-by-numbers, really, unless you embellished the heck out of it - but you could use it as a tool to build up a challenge. A challenge might seem like an exciting scene, but when you play through it, you find that the party can't make the right checks at the right time to complete it, or that everyone lacks a critical skill. The SC structure avoided issues like that, it was just another way that DMing was excessively easy in that brief period of the game's history. But, if you don't share that structure with the players, it could turn into a sort of pixel-bitching or skill-check pinata bashing, they just keep trying checks until at some point they had enough - or they could declare the 'wrong' skills too often, and fail too easily - so it was, as was generally the case, better to bring it out in the open, like a mini-game-within-a-game.
5e has no such guidelines, you can impose the structure, but with BA and DCs varying relatively little, there's no depth to the exercise played 'above-board,' and, taking it behind the screen runs into the same problems.
The traditional D&D way of handling a big ol' dungeon, OTOH, is right up 5e's alley, er, 10x10 corridor.

You map out the complex, the party explores it. They declare their way through, picking directions, chosing when & where to search and what to try, you call for checks only as needed and each check determines that isolated success/failure, by itself, not contributing to anything abstract.
It might require more prep but it plays to the strengths of 5e's resolution.
If you don't want to go through the whole thing in detail, you can just narrate large portions of it with a single check here or there, until you get to something 'interesting.' You lose some old-school immersion/player-skill feel in hand-waving portions of it, but if the backdrop is just too big to go through in detail, it's an acceptable sacrifice.