I'm not sure I'm following your logic Mark. If it came from a Chinese source why not write it in Chinese, particularly since the characters are the same in Japanese? Are you suggesting Tanamo was trying to obfuscate a Chinese connection, if there was one, by using kana?
Uh, yeah, it would seem you didn't follow my logic.
You went into an area that I wasn't even thinking about, although my thoughts run similar to yours on that topic.
Let me see if I can clear this up a bit more ...
Take a step back and let's look at the Chinese martial arts (CMA). There's a common set of phrases in the CMA. Outdoor Student and Indoor Student. The Outdoor Student is the regular person who is training with a teacher. These Outdoor Students are the people who are taught the forms. Then when a student is accepted by a teacher as a disciple or as someone the teacher wants to teach the "secrets" to, that student becomes the Indoor Student.
Now, borrowing from Dan's theory for this part (read his previous posts in this thread), what if Tanomo was an "Indoor Student" of some Chinese teacher who had Internal Skills? Tanomo learned internal structure, internal power generation, and spirals in a context that trained his body outside of any martial techniques or lessons.
Do you see how this fits completely with Shiro Saigo and his "Yama Arashi"? Not taught judo but taught aiki to make throws not seen in judo at that time.
Do you see how oshiki uchi would apply?
Let's take my theory one step further. Tanomo is told that these skills appropriately match chi/qi and Tanomo writes the katakana version of aiki because it came from a Chinese source.
Takeda then is taught by Tanomo and writes aiki in katakana just like his teacher did. Why? As Takeda was illiterate but highly intelligent and had excellent memory, then Takeda would have been able to remember how Tanomo wrote it and rewrite it the same way.