How can I specifically enqueue scripts for edit orders pages only

You can do it by checking current post_type. For woocommerce order page, post type is shop_order. So try to change your code as follows.

function selectively_enqueue_admin_script_js_for_edit_address($hook)
    global $post;

    if ($post->post_type === 'shop_order') {
        if ($hook === 'post.php' || $hook === 'post-new.php') {
            wp_enqueue_script('artio-wc-admin-order-page-mod', '/wp-content/plugins/custom_wc_mods/order_page/paste_payment_instructions_and_prompts_into_shipping_address_form_v2.js', array(), date("h:i:s"));
            /* */
            /* During development, you could avoid the hassle of clearing the browser cache by passing a dynamic variable as the file's version when you enqueue it. For instance, the current time. */
add_action('admin_enqueue_scripts', 'selectively_enqueue_admin_script_js_for_edit_address');