Not beign a student in anyway on stomach cancer, the only thing I would add to your question is the qualification that other cultures, particularly the Japanese, are not taking in just Iodine per se', they are taking in natural substances via ocean vegetables and sea foods that themselves naturally contain Iodine & trace minerals, but also contain a wide assortment of un-natural substances via pollution of the air over oceans and water in oceans and sediments at the bottom of oceans where the same ocean vegetables grow and sea foods feed.
PS - as an afterthought, there is probably reasonably good chance that another possible factor in Japan's stomach cancer rates is the radioactive fallout from bombs set off at Nagasaki and Hiroshima; possibly contributed a somewhat lasting effect to, at the least, the soil quality in and around Japan?