I'm rewriting this question because I realized it was totally unclear what I want to do. I'm looking for a way to "obscure" the theme directory so that absolute URLs that reference things like images and stylesheets in that theme directory don't have the "wp-content/themes/my_theme/" structure, but are rather more direct, like a normal website, eg: "/images/my_image.gif" and "/css/stylesheet.css".
It's easy to hard-code the path to your theme's folder using the recommended get_template_directory_uri() to programmatically bring up the theme folder, but the theme folder structure is completely exposed this way.
I'm hoping that the answer can leverage
wp_rewrite in some way, because the only other solution I can think of involves editing
.htaccess and that means hard-coding the theme directory into your htaccess file. I suppose this could be automated via a plugin or your theme activation function that edits the htaccess file, but I'm hoping that someone out there knows of a more "built-in" way to do it.