I don't know Under Hollow Hills in any detail, but know that it is different from AW - and the quote shows that.
I think a skill challenge can be used where what is at stake is the reception of sincerity.
I mean I guess you could say "I'm Persuading them of my sincerity" or something, and I'd be open to demoing that out in a game, but I'm not sure it has the lexicon of actions without getting pretty creative? At least not from the perspective I'm sitting at currently. Always open to knowing how I'm wrong

What's the issue with fiat?
Do you just want to add a dice roll or are you not sure what you'd be rolling for?
I cannot know the totality of a character acting in a world I merely create in my mind, without the physicality / body language / sincerity / & endless etc. Thus when we hit a certain "this path is in doubt" or "how will this character reciprocate" when it's not merely a transactional event (which a) likely has mechanics to cover anyway and b) I have simple tags and such to lean on), I would like a roll to help structure the outcomes instead of me just inserting something that "feels right."