In particular I am looking for companies that manufacture large quantities of engagement ring semi-mounts in these countries.
I am NOT looking for wholesalers, retailers or manufacturers that make rings with the diamonds already set in them.
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You are looking for Manufacturing Jewelers that create ring blanks that in the trade are known as Semi-Mounts or Semi Mounts. It is likely that even the large suppliers like Stuller - http://www.stuller.com/products/67769/?groupId=102618 - or Otto-Frei - http://www.ottofrei.com/store/home.php?cat=2117 - are not the manufacturers.
So two suggestions:
1) Check with some of the jewelers trade magazines like www.jckonline.com. FYI, JCK stands for Jewelers Circular Keystone. They may be able to point you in the right direction.
2) Every semi-custom jeweler that mounts loose stones carries semi mounts and has catalogs from various suppliers. Visit or contact your favorite jeweler and ask about their suppliers.
Hope that helps.