On a related note, since you seem to have a good understanding of FtD, how would you frame trying to get Haru to drop his mask in terms of social combat? Not sure which skill it should be, or what Aspect for that matter.
It would be an Empathy roll to get him to open up and admit to the Aspect of his character that makes him dislike clan kids, opposed by his Deceit (if he tries to play it off and lie) or his Rapport (if he tries to go sullen and resist admitting anything). Note that making an Empathy roll will require an empathetic approach, something along the lines of, "Come on, man, we won't get anywhere if you keep dancing around this." You could also use Provocation, but that would be to needle him into blowing up and admitting it... something that would leave him angry and afraid afterwards. So don't take that approach!
Hazou isn't great at Empathy, but on the other hand Haru must have shit Deceit or he wouldn't keep blowing it with these obvious displays of anger. Getting Haru to admit to his dislike should have the mechanical effect of us knowing the Aspect and getting a free invoke on the Aspect for having discovered it by a roll.
After that, Hazou can make a Presence or Rapport roll to try to get through to Haru. Presence would be if Hazou wants to make a speech about he knows that clanless ninjas have it tough, and he wants a village where they are valued like all other ninjas, will of fire rah-rah, won't you help Hazou take the first step? Leadership and charisma, basically. Presence would be opposed by Haru's Presence or Resolve. Hazou could also use Rapport, making the case that Hazou is "one of the good ones" and is willing to be a sympathetic ear for Haru's problems. That would be opposed by Haru's Empathy. As Hazou has a 15 in Presence but only a 10 in Empathy, he will probably want to to the leadership angle. This also allows Hazou to spend a fate point to invoke the "Idealist" part of his High Concept in addition to invoking Haru's Aspect.
Note that Hazou is not required to succeed at his Empathy roll to learn Haru's aspect to proceed on. It simply means that he will be proceeding blindly and risks have misinterpreted the situation if he didn't correctly guess Haru's issue.
Hardly anyone will voluntarily take social consequences rather than give in, so it's likely that if we overload Haru's mental stress boxes he will immediately concede the conflict and decide to trust Hazou. If we don't do some mental stress but not enough, repeated rolls may be required and he'll have an opportunity to counter-attack and hit Hazou's mental stress boxes. (Conceding being that we give up on the argument and don't bother him again.)
Note
Social skills are always mediated by the GM's judgment of what is plausible and reasonable. Using Empathy to get someone who is infiltrating as a mission to open up will likely not get you a confession, but at most some twitches and give-aways. But in this case, Haru is presumably just a kid with emotional issues who can be convinced to talk if given the opportunity.
EDIT:
I also feel like our team throwing seals around left and right in general tends to be interpreted the way Hinata did during the spar - as a demonstration of wealth. I suspect Haru was internally seething the moment Hazou brought up seals again (and we also got some weird looks from others that I'm not sure how to interpret), and Shikamaru's casual proposal to just throw money at the problem simply sent him over the edge.
Just to point out, but Haru personally witnessed Hazou making seals by the dozens in the fort. That likely softened his seeing them as a demonstration of wealth, since now he understands that Hazou is personally making the seals his team is using. (Knowing nothing about sealwork like most people, Haru has no idea how difficult any given seal might be and just assumes that if Hazou has seals he must have made them.)