I know a few folks with hypothyroid & adrenal insufficiency who have managed to lose weight on the HCG diet. But it is a very austere diet and you must a) build up a copious supply of electrolytes to prevent severe leg cramps, and b) cleanse the gall bladder because the diet contains no fats or oils and so the gall bladder won't be emptying on a regular basis during the diet.
Some people have lost weight with iodine, but you really have to have working adrenals to be able to handle the thyroid detox.
I am in the same boat you are. I went on the HCG diet but had to stop because of leg cramps. I am building my system back up now and may try HCG in the fall.