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EDITED TO ADD: What follows is very presumptuous of me. I should have first asked how you approached the challenge. For all I know, you already tried what I suggest below.

Thanks for posting this. Your original mention of the situation on Twitter intrigued me, and I'm glad you followed it up in a forum that allows more than 140 characters per response.

First of all, I haven't run this skill challenge, merely looked it over.

On the face of it, this challenge is very similar to The Negotiation on page 76 of the DMG, right down to the automatic failure from Intimidate. The Negotiation is Complexity 3, and the skill challenge in question here has a few elements that make it more complex (lower-case-c) than a regular negotiation. For one thing, the main NPC in the challenge is borderline-insane. For another, he's got an angry mob listening to him. Finally, the challenge is tied in to the mystery underlying the adventure.

So, if upper-case-C Complexity is meant to be related to lower-case-c complexity (as I think we hope it is) it makes sense for this challenge to have a higher Complexity than The Negotiation. Of course, the Complexity of the Negotiation is rather arbitrary, so this isn't necessarily a strong case for this challenge to be Complexity 5. In any case, it doesn't directly offer advice on how to justify the number of successes involved.

For that advice, though, I'm going to look back at what makes this challenge more complex. We have our crazy negotiator. Things might be going swimmingly but then the NPC says, "Yes, I see what you're trying to say, but I have to wonder why you're avoiding the issue of the hordes of spiders infesting my house!" The PCs can try hacking away at his disturbed logic with Diplomacy, but one hopes this sort of comment would lead them to try Insight to figure out what's up with this character.

(On the subject of Insight, the fluff they give for the DC 10 check doesn't seem like it would necessarily jibe with what the PCs are askng for insight into. I'd expect them to ask whether the NPC is putting on an act, or believing what he says; gauge his temper; or maybe determine what he's really upset about. If they succeeded, I'd probably tell them a little about what they wanted to know, and then mention the facts listed on that line as also having been noticed by them.)

The hostile crowd can also be used to take a negotiation that's going well and dunk it in the toilet. Even if most of the crowd is not as crazy as the NPC, it doesn't take a very large crowd to include at least one person who will shout out crazy things. So, even if the NPC seems to be convinced by the PCs, one shout from somewhere in the crowd could set him off again.

Finally, there's the mystery underlying the adventure. If the PCs feel they have convinced the NPC, but haven't passed the Insight and Arcana checks that get them to the heart of the matter, then you can ask them if they'd like to cease their efforts where they are and give them a partial success - but, as I see it, no experience or other rewards for the challenge.

Those are my basic pieces of advice for justifying a large number of successes for this challenge. During the actual challenge, when the PCs are describing their actions, there may be other things that arise for the NPCs to react to. Now, me, I like to tell the players a lot about a given skill challenge, including the Complexity and how close they are to success. Even without that, though, the DM knows how close they are and it falls to him or her to describe the attitude of the NPCs in terms that make it as clear as possible how hard this obstacle is. I feel the characters would be able to get a sense of this once they delved into the problem, so it should be a part of the DM's description as much as any sight, sound, or smell.

I realize you've already run this so this advice comes late, but I hope it will help you in thinking about other challenges you run. Look for what makes the challenge complex, then think about ways to introduce twists to the PCs. Let them know how complex the problem is, either directly or by description (unless there's specific reason why a problem should start out seeming simple and only later appear more difficult). Good luck, and I hope you decide to run this challenge or another one as a Danger Room.