I'm gonna play about with HTML Editor 3 on one of our dev servers, if I find anything out that may assist you (and others) in relation to the custom styles I'll post it on here.
Update: I've done a bit of digging around in the files and found a directory called 'styles' (located at: webassist/ckeditor/plugins/styles/styles) within HTML Editor. In this directory there is a single JS file called default.js and it's this file that contains the default styles that HTML is displaying - I tested this by adding my own additional style to it and then checking that my style was displayed in the editor and it was. Therefore the problem is a setting somewhere within HTML editor that is either not updating this default.js file with my custom styles from my stylesheet or a setting that is not being changed instructing HTML Editor to use my stylesheet instead of the default.js file.
I cannot get my custom styles to appear in the editor any other way than editing the default.js file by hand, which is obviously not what you want to be doing each time you use an instance on the extension.