I would like to be able to sort product listing by model, new to old, price etc.
This works fine with Specials, New and Featured listings but not with Category Listing.

Is there a way to have this display order function work for Category Listings?

I believe that Category Listing uses the template tpl_index_product_list.php and it does NOT use tpl_modules_listing_display_order.php, whereas tpl_products_new_default.php
does.