Using page-id-{ID} from body_class() in local dev, versus live staging

You could use slugs instead of IDs.

Taken from the Starkers theme (add it to your functions.php):

add_filter( 'body_class', 'add_slug_to_body_class' );

    function add_slug_to_body_class( $classes ) {
        global $post;

        if( is_home() ) {           
            $key = array_search( 'blog', $classes );
            if($key > -1) {
                unset( $classes[$key] );
            };
        } elseif( is_page() ) {
            $classes[] = sanitize_html_class( $post->post_name );
        } elseif(is_singular()) {
            $classes[] = sanitize_html_class( $post->post_name );
        };

        return $classes;
    }