Godzfirefly:
That said, it's not too hard to alter the official version of skill challenges to make them work as intended (to help encourage role-playing and grant a sense of challenge and accomplishment outside of combat.)
That's a good description of a desirable function of skill challenges. I think there was a common belief (including by some of the designers) that skill challenges were meant to be a somewhat mechanical minigame, and in that the concept surely fails (though I think there's probably a way to do that).
What never worked for me for skill situations before 4th Edition were:
Lack of easy guidelines for setting DCs.
Lack of easy guidelines for knowing how many checks to make.
Lack of experience award guidelines.
Lack of advice for keeping the game moving despite failure.
Roleplaying and a sense of accomplishment were fairly easy to generate in past versions, I guess, though skill situations always seemed awkward and forced to me.
4th Edition skill challenges at least covered those bases. When skill challenges in 4th Edition haven't worked for me, it has mainly been when people weren't bought into the pacing concept and wanted their one good roll to settle everything, or when players weren't particularly interested in doing things that lent themselves to skills or even ability checks.
Another key problem I ran into early on is that players tended to want to put their best character forward and let that one roll all the checks, pretty much trivializing the challenge. I think the avoidance of that was the intent behind the rules in the DMG that required participation, but yeah, that didn't really work, in general. I think I have ways of dealing with that, though I still don't force anyone to participate.
Godzfirefly:
d. Mechanics: Roll initiative. Characters will attempt to aid the party in initiative order. Any skill which the player can find a relevant use for is an option—with the following two rules:
i. A player may not use the same skill twice in a row
ii. A player may not use the same skill as the one immediately before them
iii. The player must be able to justify how the skill helps the party advance towards accomplishing the goal.
The purpose of those two (three) rules seems to be to keep players from just spamming their best skill over and over, trivializing the challenge. I understand that impulse, but the trouble I encountered was that it's not always clear in-game why a character can't, or shouldn't, or wouldn't use the same skill again, or the same skill as someone else (it was, arguably, clear enough why, say, using Streetwise to climb a cliff isn't really in the spirit of things).
So, I found that skill challenges needed a lot of description. The example in the DMG actually shows this pretty well, as I recall, with the duke's objections changing as the negotiation continues, and players rising to meet each new objection, rather than just making the same point the same way over and over.
I feel like every skill challenge has to change with each skill check, pass or fail and, ideally, fail in a way that offers a clear opening for another clearly-applicable skill (or several others). I will often have skill challenges "go on the offensive" and directly threaten or challenge the next player or a player who hasn't done anything recently. That player isn't required to act, and isn't required to use the skill or skills indicated; anyone can help them, with pretty much any skill. But I find that when I "target" players and give them a reason to have to do something, they often will, even if it's not their best skill.
The issue I've found with iii. is: Who judges whether a player's justification is adequate? Do people find that rules like that are necessary, or do they find that players generally stay "in bounds?" Do they find that players are hesitant about using certain skills, because they don't want to be told that they can't or shouldn't? Can (or should) a GM or player offer to assist a player with a justification?
I agree that skill challenges work well when they're a collaborative narrative. Apart from encouraging "Yes, and..." though, I don't know that 4th Edition encourages collaborative narration all that much. I use it a lot in D&D, but I feel I mostly get it from other games.