I am teaching in Korea now, but I have been here only just under two weeks. I have not been sick yet, but I explain to servers in restaurants and to private householders that I cannot eat gluten and explain what it is in such as flour, soy sauce, noodles and such. I never eat red paste or anything that looks red. I stick to rice and vegetables. Koreans eat very healthly and eat lots of raw fruit which is great for non-gluten diets. They also eat salads, tofu and vegetables barely cooked. Again, I have been here less than two weeks but no problems so far. There is a dish that is rice and veggies one can always count on and I have been to Korean barbecues that went great as well.
I am trying to speak Korean as fast as possible so I can say "hold the hot sauce."
Koreans eat very healthy and as long as you avoid the red paste and noodles, bread things should be fine, I hope. Of course, always inquire about soy sauce.