After all the fiddling, I've finally got Cortana working on Windows 10. Yay. :S
Thanks to these instructions, I guess the missing bit was installing the speech files for the selected language. I have to say that I still find it strange that English (US) is considered a completely different language to English (UK) or English (Australia). Balkanization all over the place, it seems.
So, anyway, installing English (Australia) speech files made Cortana finally work with Australia as the selected region and English (Australia) as the default language.
Now let's see what it can do. So far not impressive.