May need more selenium, I get about 400mcg daily from supps and been supplementing Lugols for about as long as you with no issues.
That being said fat distribution is based on more than just Iodine and thyroid function. Perhaps you have high estrogen levels, high cortisol or who knows what.
Paleo diets due to limited selection of food can make one miss quite a few nutrients, potassium certainly comes to mind.