How to modify the default feed via a function

You could try out the template_redirect action to overwrite the default feed template:

add_action( 'template_redirect', 'custom_template_redirect' );
function custom_template_redirect() {
    if (!is_feed()) 
         return;

    header('Content-Type: ' . feed_content_type('rss-http') . '; charset=" . get_option("blog_charset'), true);

    // your own template stuff here 

    exit();     
}