I'm having a little trouble understanding exactly what you're saying in that first sentence... the lack of punctuation makes it a bit hard to read. But, if I'm following you correctly, you're saying that the Bujinkan schools all rely on similar things, such as Ichimonji no Kamae, yeah? Honestly, I'd disagree with that pretty much out of hand. In essence, you can break the Bujinkan schools down a few ways, one of which is to look at relationships between the arts themselves... which gives us two primary groups (that I think of as the Hakuun grouping and the Amatsu grouping).
The Hakuun grouping is Togakure Ryu (Kain Doshi, one of Daisuke Togakure's teachers, was said to have taught him Hakuun Ryu), Gyokko Ryu (founded by Hakuunsai Tozawa of the Hakuun Ryu), Koto Ryu (founded by the 12th Soke of Gyokko Ryu), Gyokushin and Gikan Ryu (also from Gyokko Ryu), and Kumogakure (related to Togakure Ryu); and the Amatsu grouping is Kukishin Ryu (directly related to the Amatsu Tatara), Takagi Yoshin Ryu (taught alongside Kukishin), and Shinden Fudo Ryu (also associated... with a couple of different theories as to how...). As a result, each of the groupings have their own similarities... but it doesn't necessarily cross over from one grouping to the other. Ichimonji, for instance, is fairly central to the Hakuun grouping, but not the Amatsu ones... same with the Kihon Happo (coming from Gyokko Ryu). The postural concepts (deeper, lower, higher etc) are particular to the different Ryu... there are similarities between, say, Gyokko, Koto, and Togakure... but Shinden Fudo Ryu (Dakentaijutsu) has none, Kukishinden is quite different again, Takagi is yet again a different set of principles and ideas. Some are armoured systems, some aren't. Each have different distance concepts, different rhythms, different tactical applications, and so on.
When it comes to the systems taught by Kawakami, I haven't seen much, and what I've seen didn't really thrill me (then again, it's often been said that Kawakami's bujutsu is average at best, as that's not what he focuses on), so I haven't looked too much in depth at much of it... but, as there's no real connection to anything in the Bujinkan, I'd highly doubt that there'd be much beyond some superficial traits that are more about them both being Japanese systems shared between them. I wouldn't expect anything along the lines of a Kihon Happo (some basics, Kihon etc, sure... but the Kihon Happo is a specific ideal and concept to Gyokko Ryu, not anything to do with any other art).