Oh goodness! <3 Flattery!
Yeah, research into East Asia is difficult because of the language barrier – and that’s just the beginning. Japan should be a little easier than China, though.
So with my initial Google searching, I found this website with a variety of publications written in both Japanese and English, which may be helpful.
My next step would be to look at museum collections.
The Tokyo National Museum has a 14th century pouch that has braided cord: [Link].
The Portland Art Museum had (at one point) an exhibit on Samurai that featured some kumihimo. They cite a book, but also feel free to reach out to the curators for more information: [Link]
Don’t limit yourself to the search term “kumihimo.” It’s translated most often as “braided cord” so don’t be afraid of using that term, especially in western museum collections.
Lastly, connect with other SCAdians who do Japanese crafts. There is a Facebook group for SCA Japanese, so someone there might be able to help.
Happy braiding! <3