Piers: I realize that this is a very old thread but I just joined the group and noticed your beautiful Jingasa with the star cluster on top. I am a collector of swords and fixtures. As such, I have seen this constellation many times depicted on various items and I have a very nice Sukashi Tsuba with it. However, I do not believe that it depicts the constellation Ursa Major. The open star cluster Pleiades, known as the Seven Sisters, is very well known in Japanese history. It is located in the Constellation Taurus The Bull and always depicted as shown on your Jingasa.
BTW, this thread was very interesting and helpful but I looked at it to see if there was a specific name for the pillow and ear loops that are laced into the Jingasa. I have an Edo Era Zunari Jingasa that is missing the pillow/straps and would like to find a replacement. Thanks very much.