Seaweed is a rich Iodine source. I have dulse, and I have the kelp powder, that I've encapsulated.
I take a lot of it per day, only started taking 1-2 tb per day, and have noticed a difference.
You can eat a lot of seaweed, it's gentle and couldn't giving you those types of reactions. Good to know though because I always felt out of loop with the Lugols, but hearing from you and this thread, it doesn't seem to be something that works well with the body, or is too harsh.
If you buy the kelp powder and cap yourself its cheaper than buying several bottles, because if you want to do a high dose thats the easiest most economical way. Taking a few caps of kelp supplement I don't think is enough.