Custom WooCommerce shortcode to display product image gallery

Question

I have been tasked with duplicating a WooCommerce product gallery in an internal page (not a product page). As such, I decided to create a Child theme and write a new shortcode into my functions.php file which would pull in the gallery template from WooCommerce.

All this has worked great so far except that the gallery does not display as a gallery - it simply displays all the images at full size with no additional formatting. Am I using the wrong template? I've been using /templates/single-product/product-thumbnails.php (default - no modifications). Do I need to include some extra libraries?

Here is what I have in my child theme's functions.php so far:

<?php
// these lines just pull in styles from the parent theme
add action('wp_enqueue_scripts', 'enqueue_parent_styles');
function enqueue_parent_styles( ) {
  wp_enqueue_style('parent-style', get_template_directory_uri().'/style.css');
  }

// here is where we add the shortcode
add_shortcode('woocommerce-gallery', 'woo_gallery_func');
function woo_gallery_func($atts, $content) {
  ob_start();
  $path = WooCommerce::plugin_path();
  global $product;
  // this creates a new WooCommerce WC_Product object
  // specs: https://docs.woocommerce.com/wc-apidocs/class-WC_Product.html
  $product = new WC_Product($atts['id']);

  // pull in the template. both options only display 
  // large images, not a gallery
  //include($path.'/templates/single-product/product-thumbnails.php');
  wc_get_template('single-product/product-thumbnails.php');

  $output = ob_get_contents();
  ob_end_clean();
  return $output;
  }
?>

To use the new shortcode, I use something like [woocommerce-gallery id="21"]