No idea about Mac-specific programs. As an emergency workaround, I suggest going low-tech. Use any simple local word processor, forget about autosave and word count - you can teach yourself to save manually from time to time, and checking word count after every paragraph is not helpful to productivity ;) Just make sure that it can work with big files, by opening and saving any big file.

Post the chapters separately, to any site which is accessible through a web browser, such as DW, and use a browser Javascript bookmarklet to count words - for example, this one: http://www.marklets.com/bookmarklets/Word+Count.aspx It counts words in a mouse-selected region of a web page. For the total word count, use the calculator.

Hope you'll be able to finish it soon! If anyone deserves to call this Nano a win, it is you :)