I started on Iodine
something like 2 years ago.
I was also on 200 mcgs of Synthroid and had been on Synthroid for about 7 years or thereabouts.
Over the last 2 years I have reduced my Synthroid to between 50 mcgs - 100 mcgs a day (according to energy levels), slowly, and guided by my own sense of well being.
My levels, when checked by the "doctor" always come back as within normal range.
In the early stages of Iodine
supplementation I did have the side effects which are supposed to be rare, but I think are more common than are stated: i.e, increased snot pardon the french, and metalic taste in the mouth as well as iodine mumps at the side of the neck.
After 2 years of supplementation, I feel unbelievably good. My thyroid (I only half half following surgery some years back) has reduced in size, and the nodules have also reduced in size. The big gain is that I have no pain in my thyroid at all (after many years of almost daily chronic thryoid pain aka thyroiditis).
Best of luck