Ignoring for a moment that I can't prove a negative, there's a number of things to understand. First is that samurai were in the employ of various Lords (Daimyo). They were, therefore, only able to train in arts that were allowed by the lord themselves... in some cases, that would be very limited (most notably to what were called Otomo Ryu, or "house schools"). Additionally, in many cases (particularly during the more war-ridden times in Japanese history), many, if not most arts were what were called Sogo Bujutsu... these were "comprehensive schools", which taught a syllabus comprising of multiple disciplines, so there was no need to go around learning sword from one person, spear from another, and so on. There's a lot more (such as what the schools were, why different arts would be trained, if at all, and so on), but that's enough for now I feel.
Edit to add, You still have not explained how techniques learned for weapon a, translate for weapon b. Say spear and sword. Different as night and day, movements for each are not similar. They are 2 separate arts.
That brings us to the idea of Sogo Bujutsu. The way a Sogo Bujutsu school is set up is that there are certain underlying principles and concepts which are distinctive to that particular Ryu-ha. In other words, learning Katori Shinto Ryu, the Kenjutsu shares the same principles, concepts, and mechanical ideas (as much as possible) with the sojutsu, the naginatajutsu, the yawara (jujutsu), and so on and so forth. In fact, it's this very fact that it all matches itself that makes it work... taking X-Ryu kenjutsu and Y-Ryu Sojutsu and trying to put them together doesn't work at all... a warrior class who depended upon skills learnt for survival would never actually try it, as it'd be suicide.
From there, I'm going to highlight some details of each of your videos, as the simple selection given here shows a lack of experience, which is honestly part of what I meant when I said you were out of your depth here. I'm always open to being asked for clarification of anything I say, but arguing with me when you aren't aware of what you're talking about yourself is, well, not such a good idea.
These guys have no actual training in Sojutsu, and barely any in most other things. The clip is filled with huge numbers of flaws, stemming from both a lack of experience as well as a lack of understanding, and incorrect assumptions based on compromised weapons being used. To read more about this clip (and these persons), see here:
http://www.martialartsplanet.com/forums/showthread.php?t=97845
While this is a Bujinkan group, exactly where the Sojutsu comes from is a question... the most likely candidate is that this is an approach created by Takamatsu, based on Bojutsu (which is kinda backwards to most). There's only one system I've come across that looks similar to the Bujinkan's form, which is Saburi Ryu... a much later development.
Again, this is a fake group. The Ogawa Ryu is a fraudulent "system" created in Brazil about 25 years ago by mimicking what they thought Koryu did, and missing some vital aspects.
In other words, none of these are good examples of Sojutsu, nor do any show a real contrast with any other weapon forms.
Say... here's a few clips that show sogo bujutsu, including a range of methods:
Kashima Shinryu - Kenjutsu
Kashima Shinryu Jutte and Jujutsu
Here, you can see the connection between the Jujutsu and the weapon arts.
Katori Shinto Ryu, showing connections between Kenjutsu and Naginatajutsu (and similar ideas are seen in their Sojutsu, for the record).