Sorting WordPress taxonomy list by natural order

I’ve followed the instructions found on the official WordPress site to create a page that shows a sorted list of one of my taxonomies. It works just fine, except I’d really like to have Natural Sorting if possible, but in the wp_list_categories function, the only valid options for the “order” argument are “ASC” and “DESC.”

I’ve tried modifying the function by applying a natural sort to the array using the following without success (returns an error):

$categories = get_categories( $r ); // this line is part of the original function   
foreach ($categories as $key => $row) {
    $sortNames[$key]  = $row[1]; 
}
array_multisort($sortNames, SORT_NATURAL, $categories);

Here’s what the first element of the $categories array looks like in a dump (I’m sorting by “name”):

array(389) 
{

  [0]=> object(stdClass)#363 (15) 
{

   ["term_id"]=> &string(3) "541"
   ["name"]=> &string(17) "2° Ms. astron. 1"
   ["slug"]=> &string(13) "2-ms-astron-1"
   ["term_group"]=> string(1) "0"
   ["term_taxonomy_id"]=> string(3) "567"
   ["taxonomy"]=> string(13) "manuscript-id"
   ["description"]=> &string(0) ""
   ["parent"]=> &string(3) "540"
   ["count"]=> &int(1)
   ["cat_ID"]=> &string(3) "541"
   ["category_count"]=> &int(1)
   ["category_description"]=> &string(0) ""
   ["cat_name"]=> &string(17) "2° Ms. astron. 1"
   ["category_nicename"]=> &string(13) "2-ms-astron-1"
   ["category_parent"]=> &string(3) "540" 
 }