Very interesting, such a great reasoning work from yours! But you didn't tell much about Billy and Fusae Campbell, who was probably adopted in the Haneda family just like Shukichi! ;)
And do you really think Rumi could be Vermouth in disguise? With so many karate skills, with Bourbon, and so on? ^^ And Ai who finds her reliable and harmless?
Following your thoughts, could that mean Wakita is Iori's kagemusha? So that matches Ai's testimony with the three depictions (Wakita isn't feminine, but Iori is, and is probably very old in truth, and with a imposing look, and he looks like a horse actually...).
I also think that guy in the car can't be the Boss, who can't show up so easily (he's supposed to have departed from this world...). But could Mr. Karasuma actually have rejuvenated into Chikara Katsumata?
Oh, and about Iori concealing his true age, it's most probably true but...did you know about the Seito Sakakibara case in Japan in the 1990s? That 13/14-year-old teen who murdered and butchered young children and who hated school and police? Iori could have been 13 back then in New York. Just like Ai, he was a young prodigy...in killing. He may have already been lying about his age to get hired by Amanda Hughes and stalk her unnoticed.
Once again, kudos for your theories!!