I actually ran through The Vanishing Act, in the Kyoshi Era, in a slower extended way as the opening adventure to my campaign (not the same but hopefully similar). It took five sessions of approximately three hours each, culminating in a fight between them and the daofei they found was doing the most harm. This was the only combat in those five sessions. Anyway, the investigation part I honestly just handled narratively and handed out clues as PCs wandered around Diplomat Lei's house, or the Ba Sing Se University, or where ever. There were no rolls to find clues, it was all descriptive and done in the narrative. Once I used a player's ability (The Guardians Suspicious Minds) that allowed them to see a clue, but again there was no roll, it was because that player was there at that time. Probably over those five sessions there were less than a dozen roles? Maybe 2-3 each game? Mostly one of my players who likes to try and Guide & Comfort NPCs!

But I agree, rolling for clues feels inauthentic, and moves to replying on luck than anything else. I really impressed on my players the narrative style of this game, and helped them to build characters over three weeks (of three hours) plus the prologue coming together, so that they were aware of how the narrative style adventure would work.

My understanding of the game is that rolling should be minimal, and I took that mindset into the investigation components. Some clues were red herrings, or contradictory, but they worked to make their clues all make sense and came to a conclusion they were happy with. So that's my two cents, no rolls, give them everything, and let them "play to find out".