My Kobo turns out to have no Japanese font, only a very limited selection.
I have followed the instructions on
this site to download and install a Japanese font. I used
Unifont. While I wouldn't recommend it aesthetically, the book is now displaying correctly so the method is sound.
I also inspected my existing Japanese content that (as mentioned above) was already displaying correctly. This turns out to be in html format, and presumably these are processed differently from epubs.
Is it worth me explaining the context of my problem for future readers? If so, should I do so here or on a new thread?