I have to disagree on several fronts.
a)You're assuming that Vermouth was interested in finding Asaca but then why she was absent/showed no interest in Hotta Gaito case? Instead we see Gin taking note of Kogoro's involvement. Also why would Vermouth assume that the old APTX had the same side effect as the new APTX? To be precise from Gin comment in the first chapter, Gin termed APTX as a brand new poison developed by the R&D, while it was just a copycat product of old APTX which was used as poison. So Gin knew nothing about that old APTX, so it's very unlikely that Vermouth knows about it, also. If Rum attacked Asaka with APTX, then he would have to divulge it before BO, so then BO would have been pretty edgy about Asaka, but we see BO getting edgy about ASACA, so BO is only edgy about the dying message not in Asaka. Else Hotta's case would have been closely monitored also.
b) The glaring mistake you made during comparing the Subaru and Rumi's conflict resolution style was Haibara's reaction during the event. In Subaru's conversation with the culprit ,she felt pressure and Dokkun, but in Rumi's case it was only astonishment.
c) The murdering intent which Rumi showed when she heard the word prosthetic/the phrase containing prosthetic and Haibara felt pressure. But Kuroda was also there keeping a close watch on them. I find it quite intriguing, I think Kuroda is the cause of Dokkun else Haibara would have felt it from Rumi during her conversation with the culprit.
d)In past Haibara was unsure of Pisco's affiliation as his smell was quite weak; Haibara got frightened of Kuroda but thought that he doesn't exude the BO aura and reasons that if he was Rum by now she would have been killed.
The Haibara's line of reasoning shows that she has ruled out Kuroda as Rum, but there is a tinge of uncertainty. Haibara isn't a kid, she has seen much more shit than Ayumi, yet getting afraid of Kuroda is a bit too much. Being unnerved isn't getting afraid though.
e) About the glass shard, I tried to do some calculation on it's possible dimension, a glass shard of that dimension and width(0.5 inch X 0.2 inch X 0.1 inch) can't be that prominent stuff peeping out of the pocket.(I used my GF's hand-mirror as the possible size estimate.)
f) Rumi's personal hatred against Rum isn't explained by this speculation of yours. You speculation is also silent about how Rumi got the glass fragment but not the shogi pieces? It seems like from your speculation that the crime scene looked more like a RPG guild bazzar where people dropped in and took things just as they like.(Rum, Akai-senior, Asaka, Vermouth/Rumi)
g)Rumi's glare even before Kuroda opened his mouth doesn't get explained by your assertion.
h)Rumi can very well be the "Bartender Girl" from 100 files ago who like Whiskey and knows that Conan is the brain behind sleeping Kogoro.(so let's not emphasize on what are personal preferences of the characters and instead look for their interactions and reactions with each other.)
i) For Wakita, I think you're taking huge leaps. I think only three files aren't enough to build suspicion around Wakita. By the way there's no surety that Wakita isn't Rum. Rum knows that Kogoro was involved in the Soul detective case so it's very logical for Rum to sniff around Kogoro.
j) The injury in his left eye seems fake to me, because when Conan asked him he readily tried to open the eye-patch which is very unwise during eye injuries. Wakita wears the eye patch because he wants his eye to be protected from outer contamination but simply throws it away in trying to show the injury to Conan. It suggests that Wakita's injury isn't fresh nor healing. It's either an old scar or injury.
k)So it can be Wakita's ruse to lure out Kogoro by faking an eye injury and thus knowing his knowledge about Rum, not an injury caused by Mary.
l) Wakita can very well be a coach like figure, to Akai-san also. Like the person who inspired Akai-san to practice Jeet-Kun-do.
m) Wakita firstly wanted to escort Kogoro to the latter's next murder case, mind it not any case, only next murder case.Which immediately spooks out Kogoro. It's more like that he wants to keep an eye on Kogoro when Kogoro is solving a murder case, not investigating Kogoro's whereabouts. It can mean many things, let's hear Gin's statement that "If Kogoro is the demon then we'll have to finish him when he sleeps." so Kogoro might be attacked when he's "Sleeping Kogoro." and Wakita wants to stop that.
n) That thing which binds both Mary and Gin can also be Akai-senior. He said the stuff to his wife and then infiltrated BO and became a mentor to Gin and said the same stuff to him. My current speculation is Wakita is probably Akai-senior and the ally whom Ethan Hondou told Kir before his death.
o) Iori fits the Asaka profile without much problems, his stealthy nature, womanly looks, Asaka's index finger being shorter than Asaka's ring finger, belief in his own prowess in hand to hand combat(in the cafe he was ready to take on the armed culprit even in the dark.) is very bodyguard like qualities.I personally think he's a lackey of Rum doing the bidding for Rum
p)I think the main person whom we are missing out on this is Kuroda and Chikara Katsumata. Kuroda is probably a NOC who infiltrated BO,whose mission was to capture Rum. He now is disguising as the Kuroda and Chikara Katsumata is Rum, the weakest horse in this whole race. It's a fight between Kuroda and Chikara.