Fyi, for anyone else with this question, there is one more step. I would have guessed just publishing the CSSMenuWriter folder would work too as the dwt template's only references to the menu were:
<?php require_once("../CSSMenuWriter/cssmw/menu.php"); ?>
<style type="text/css" media="all">
But when I published up the CSSMenuWriter folder I got this error:
Fatal error: require_once() [function.require]: Failed opening required '../../webassist/framework/library.php' (include_path='.:/usr/services/vux/lib/php') in /data/25/2/98/45/2424045/user/2657060/htdocs/spyglasscondos/CSSMenuWriter/cssmw/menu.php on line 4
So I published up the webassist directory as well. As far as I can tell now, it all seems to be working well.
Thanks, Jason. This was much easier than publishing up the whole site.