The new materia system Yoshida brought up will give the ability to add +atk and all that stuff. But youre on to something with turning a NQ complete item into a HQ item by means of a different mini game or 'improve item' system.

Tho, with the materia system coming out to customize equipment by socketing it, they should probably just do away with the HQ system all together. Socketing items to increase their power would be making them HQ in a way.