Kona Cottons usually have the fuzzy edge, but not always. Sometimes they have a flat edge with 'tooth holes', but not what I would call ribbed.
Be aware that KQ carries several different brands of solids...Kona Solids, RJR Supreme Solids, Moda Bella Solids and Marcus Brothers Centennial Solids are the main ones. Their stock numbers give no hint at all as to who the manufacturer is, the customer service folks aren't ever given manufacturer information, and worse yet they put stickers over almost all the info on the bolt end in the store. I'd try the Marcus Brothers first.