I stayed up way too late one night thinking about this and writing it down in my commonplace book, so please bear with me. Is Sir Barrymore Feint principal of Prufrock Preparatory School?
I know it sounds crazy but think about it. The music that Snicket heard sounded both odd and familiar. We know Sir Barrymore Feint (SBF) was a violinist and part of the Prufrock Prep staff for some time. What if he was the one who was playing the tune? Being a musician he could have easily given a music box with the music he had written or played to anyone. This leads me to my second point.
The music box is initialed A.F., right? For Armstong Feint, right? What if Hangfire is not only SBF's son but part of the Inhumane Society together? Does that mean that SBF could've been playing the tune to attract recruits Ishmael style? If so, how many other music boxes could've been made? Is the tune an important feature of the Inhumane Society like our codes and poems? If all this is true, why a school of all places?
On a similar note, there is no way that if he was playing his violin at Prufrock Prep while being the principal he didn't know who the Snickets were. If he knew the family, when Armstrong saw Lemony get mixed up with Ellington he could've warned him. And if he was part of the Inhumane Society, he could've also known that the other V.F.D. kids could not be trusted and maybe tried to serenade or brainwash them with the tune. I don't know. That one seems a little out there but still.
Snicket and Sir Barrymore Feint are definitely connected in some way, and I think that this is really the only way that entirely makes sense. I still feel like I'm asking the wrong questions.
The world is quiet here.