So the 'events' weren't a one-off thing... Reqeusaet en fancy suit. This 'Invisible Man...' Could it be that they're....
TARGETTING THE SNAPPIEST DRESSERS?!
Well, that's me, done. Ahahahaha!
More seriously; Ashdown and Tronen's chat was another one of those really effective little moments, which made the stinger + ensuing mystery that much funnier. And speaking of the mystery, this one was one of my favourites; I'm really loving how it's not just 'wait, we forgot something' and that you can see the Fourth-Class detectives really working to keep up.
Also, I learned how long it takes a person to die of dehydration! Thanks, Ashdown! That is a Fun Fact!
I did better in the second half, rather than the first. And I was sorely tempted to believe that somehow, in some manner, teleportation was involved. On the other hand, going unnoticed can be a kind of teleportation, though that's not really relevant to this mystery, is it...
The Game-master chapters have also been really enjoyable of late, and the phrase 'Detective (Detective) Revolution' is something I never even knew I wanted to read. If you've the time and interest on including the rules for Catapult the Calendar in the finished product, I think that'd be a sterling supplementary material.
Closing up, I actually have a few hunches, but - keep it up! You're making great pace, and I've been enjoying every step of the way!