As the 2nd title says, it is not a mystery but an improbable tale. On the surface it is the unveiling of a conspiracy, but the writing is sarcastic and doesn't fit to a mystery plot. Later we see it is an experiment in trangenderism not unlike Virginia Woolf's Orlando. Not for everyone and mostly silly.
The author tries to imagine what a detective does in his daily work: mainly suspense. The case works out by itself, indeed, with the detective almost being a bystander, so in the end it comes close to reality. What's interesting if you're not into the included romance is the extensive description of the Chicago World's Fair of 1893.
Stopped reading after 100 pages, as it all took too long to develop, and in both realities described the respective protagonist continued to be painted as most stupid. With not much more than a teen tragedy in sight, motivation failed me.
Found this quite satisfying and very unlike many attempts from the pulp genre. You can just see that this author took himself the time to develop the characters right. Recommended.