I just tried to set the template for a shortcode, and discovered that your shortcode function strips out the template parameter. This means that shortcodes can only get the default template. I reckon it would be useful to some people if you allowed this parameter, so that they can have different login forms on different pages, for example.
I got done what I wanted today by creating a separate template for the widget, which does support selecting a template, and using the default template only for the shortcode (I only need one). So still this is a very flexible plugin :)