I want to display FIRST in stock items THEN out of stock items. Within those two groups, the products should be alphabetized. https://www.dropbox.com/lightbox/home/Public
Check this link out may be this is the thing which you are looking out for
[1]: http://tareq.wedevs.com/2013/12/woocommerce-sold-out-badge-on-products-listing/
Separating sold out products