Thanks, Doitsu. Kepub works! I didn't want to go down that route, but it's the only way it seems. (I just hate that enforced header in kepubs...)
Interestingly, the Kobo picks the regular epub renderer for your epub3 and makes the same mess of it. Isn't the regular Kobo epub renderer supposed to be ADE/RMSDK? Why does it work there and not on the Kobo? I'm so glad I don't have to do this for a living (Hi Hitch
)
And I solemnly vow to finally update my Sigil and start exporting to epub3. Been putting that off long enough...