4.4 is an all or nothing version which requires attribute stock to be set up for all attribute combinations, or they're treated as zero and orders then go to backorder.

Download version 4.6 (not 4.7) and take replace only your includes/functions/functions_lookups.php with the one from the newer version.

This is the change that allows the product level quantity to be used when no attribute level stock has been set. The change was made for a client in a very similar position to you and is working perfectly for him.