I had a dog with hypothyroidism. She lost hair down her back and had crusty sores. If it is indeed a thyroid issue, the Iodine would definitely. Have you thought of putting the Iodine in his food or water?
Humaworm sells a medicated cream that might help the skin issue. It would help with mites, if that is what it is.
Skin problems caused by thyroid problems can become major problems because of the bad immune system. Skin infections can become pretty bad. Keep a very close eye on it. Personally, after hearing about the hair loss and crusty spots, I would take him to the vet and have blood work done / thyroid test.