I want to caution people about getting thrown off by "Fusen-ryu". The confusion is caused because the 4th Soke of Fusen ryu (Mataemon Tanabe) refined a personal newaza system years before he inherited that ryu-ha. The people beating the Kodokan on the ground used this system, but flew the Fusen flag (because of their master's title). It's a red herring. As is Kosen.
Definitely the timing of the actual Kosen format as we know it is a bit late to have influenced people like Tani, Uyenishi or Maeda. Tony Wolf of the Bartitsu Society has done some interesting work on early scholastic formats of this sort.
There are a few key moments where certain hypotheses can be rejected in favor of a better model. For example:
the idea that Helio, Carlos or any Gracie in particular substantially modified what was taught at Maeda's club in Belem is contradicted by the existence of the Franca/Fadda Maeda lineage, which is essentially the same art (at least in terms of newaza, if not atemi), and was so when they first encountered one another. The distinctive properties of Gracie Jiu-Jitsu newaza can not come from a special contribution from the Gracies, or else we would see this difference when contrasting it to the newaza of the Franca/Fadda branch of Maeda's students in Brazil, and we do not. And so we conclude a common source for both branches: Maeda.
Similarly, Kodokan Judo can not be the source of the newaza practiced by the Japanese challenge wrestlers in England (there is no evidence they received any Kodokan training at all), and yet we can see many features present in their newaza that are similar to both the Fadda and Gracie lines of Maeda's teachings. Maeda spent significant time traveling with Tani and Miyake, and we can suppose that there was a sharing of technique.
But if this were the end of it, we would expect not to see this same similarity in the newaza popular in the Kosen format (which came long after this sharing of technique would have ended). And so again, we are led to postulate a common influence. It can not be the original Kodokan newaza, as Tani, and Uyenishi had no exposure to this, and it can not be Kosen newaza (which came later); it can only be something present in the backgrounds of both Maeda, Tani and Miyake. This is not something from Maeda's Kodokan background that Tani and Miyake shared (Tani was explicit that any knowledge he had of the Kodokan's material was tachiwaza only), and so it must be something from Tani, Uyenishi and Miyake's background that Maeda shared. Is there such a syllabus of material that resembles in it's description the newaza of both the challenge wrestlers in England, and that of Maeda and his lineal students in Brazil? Tani, Miyaki and Uyenishi all point to a newaza-centric approach associated with the city of Osaka and the names Matemon Tanabe and Yatarou Handa as the source of their training. And the syllabus of of Mataemon Tanabe is known to have been revealed to members of the Kodokan after it suffered numerous by defeats by Tanabe and students using his approach. This then is the obvious candidate. Moreover, the Kosen format newaza that also bears a strong similarity to the other branches of newaza under consideration developed through the efforts of two principle figures, one being the only person known to have fought Tanabe twice (and the only one to have fought him to a draw), making a study of him and dedicating himself to newaza practice as a result of the challenge Tanabe faced. In fact it is very likely that this person (Isogai Hajime) is one of the Kodokan members Tanabe revealed his syllabus to.
The only reasonable alternative to this model is numerous, independent instances of parallel evolution at different times, and in different locals, all producing extreme similarity. Some would argue that similarity of rules and format (specifically the absence of pinfall and Ippon) creates this parallel evolution, but I intend to argue that the specific features of similarity are much too close for this to have been the case. After all, most human instinctive and playful grappling is free of Ippon rules and pinfalls, and yet we do not see these features distributed universally around the globe, or discover them as children. Similarity of format may produce a slow evolution towards similarity, but a common input of technique and ideas creates a center of gravity around which a cluster of distinct styles might orbit.
(cont...)