There were two things that were causing this problem for me. First was the disabling of anti-aliasing fonts in CoreGraphics (fixed by Jules in commit 74f8c9b, via another forum thread).
And secondly, in my AudioProcessorEditor constructor, I added the setting of the default look and feel on the desktop instance with Desktop::getInstance().setDefaultLookAndFeel(customLookAndFeel); to ensure that my overriden getTypefaceForFont actually gets called, i.e. my look and feel setup looks like this:
customLookAndFeel = new CustomLookAndFeel();
I dunno if that's correct but my fonts are now right.