I just found what is arguably a cleaner way to do this…thanks to this other WPSE question How do I add a php statement to a jQuery string.

I never new about wp_localize_script() until reading the answer to that question (I love WPSE :-).

PHP

add_action ('wp_enqueue_scripts', 'localize_js') ;

function
localize_js ()
{
    global $post ;

    $args = array(
        'post_type'      => 'page',
        'posts_per_page' => -1,
        'post_parent'    => $post->ID,
        'order'          => 'ASC',
        'orderby'        => 'menu_order'
        );
    $subservice = new WP_Query( $args );
    $slugs = array () ;

    while ( $subservice->have_posts() ) {
        $subservice->the_post();
        $slugs[] = $post->post_name ;
        }

    wp_reset_postdata () ;

    wp_enqueue_script ('my_script', plugins_url ('js/my_script.js', __FILE__), array (), false, true) ;
    // wp_localize_script() will handle the outputing of the relevant JS global decl
    wp_localize_script ('my_script', 'my_slugs', array ('slugs' => $slugs)) ;

    return ;
}

JS, my_script.js

$('#pagepiling').pagepiling({
    sectionSelector: '.box',
    anchors: my_slugs.slugs,
    menu: '#menu'
)};