As a sanity check, I converted again but with font size scaling enabled. (I disabled it earlier because my chapter headings were being shrunk). Suddenly all the generated font-size rules are expressed in ems instead of points, and it looks sensible again.
So it would seem that there is no way to get the font sizes in the EPUB accurately translated to the AZW3 -- either I end up with sizes in ems translated into incorrect sizes in points, or I let it change font sizes in ems into different font sizes in ems. Apart from which, it also changes my margins, whether I use font size rescaling or not.
It looks like I'll have to go for font rescaling, and waste another three days reconverting everything, unless someone can suggest an alternative...