Override core WooCommerce function

I am using WooCommerce, and I have a custom order status to which all new orders are assigned (instead of the default "Processing" status). The WooCommerce admin menu shows a helpful tip showing how many orders you have that need attention, but it only counts "Processing" orders. I want to make the count reflect my custom status.

• The function that gets the count is wc_processing_order_count() and is defined in woocommerce/includes/wc-order-functions.php. No hooks or filters.


• 
  

  The function that displays the count is menu_highlight() and is defined in the class WC_Admin_Menus. The menu_highlight() function is hooked in __construct():

  
  

  
  add_action( 'admin_head', array( $this, 'menu_highlight' ) );
  
  



• 
  

  The WC_Admin_Menus class is not stored in a global variable when instantiated, and so there is no easy access to that hook.

  
  


• 
  

  I want to make the change without editing the core WooCommerce files, as they will be overwritten on update.

  
  

I was able to remove the 'admin_head' action using this function. Then I could customize the menu_highlight function and the wc_processing_order_count. Is there a more straight-forward way to do this?

function remove_menu_highlight() {
    remove_filters_with_method_name('admin_head', 'menu_highlight', 10);
}
add_action('admin_head', 'remove_menu_highlight', 11);
add_action('admin_head', 'custom_menu_highlight', 12);