CHK91 has good advice, but I also think it's good to try out the different extremes too, just to see how they affect you. If it doesn't feel right for you though, you shouldn't continue with it. Plant foods aren't completely bad, though I prefer fruits over vegetables, since fruits are specifically created by the plant for the sole reason to be eaten.. while most vegetables are harder to digest and contain anti-nutrients. But if they do good for you, then you should eat them.
as far as sources of iodine, I would suggest egg yolks. In my opinion, egg whites are useless and unneeded, and I hate the texture of them anyways unless cooked.. so I don't usually eat egg whites. But if the texture is fine for you, you can eat them, just most of the nutrients are in the yolk. I'm not sure about manganese, but you could always go to nutritiondata.com and look up any specific nutrient, then sort by meats/dairy and such to filter out all the plant foods.
but why don't you want to include fish meats? sushi is good, I recently tried some sashimi(which is just pure raw fish meat, no rice or seaweed or anything added) and it was quite tasty.. I like yellowfin tuna the best I think, since it's nearly the same texture as raw beef.. while the albacore(sp?) that I tried had the texture and taste of chicken! I don't like that taste or texture of any crustaceans though, such as shrimp, crab, or lobster.
