Partly solved.
Apple wants some additional standard in epubs intended for iBooks, META-INF/om.apple.ibooks.display-options.xml
Code:
<?xml version="1.0" encoding="UTF-8"?>
<display_options>
<platform name="*">
<option name="specified-fonts">true</option>
</platform>
</display_options>
This actually works, but now it disables the ability to switch between justified text and left-ragged. GAH! Well, text-align: justify fixes this.
There's also am official iBookstoreAssetGuide.pdf, easily to be found with a web search.
Specifying your own fonts doesn't disable using the system fonts, by the way, it adds another entry to the font selection menu “original book fonts“ or somesuch.