I also had problems with constipation with iodine. Newport suggested that it may be heavy metals...lead in particular. I think that metals may be an issue for me...and the Iodine is a potent chelator. I addressed the constipation by increasing my magnesium intake.
I also wonder...for myself...about the effects of Iodine on my GI flora. I stopped taking iodine, did some light colon and kidney cleansing...and started really hitting the probiotics. My digestion has been improving ever since.
As for iodines effects on hormones...again, for me...these are more questions I have. I am already perimenopausal and I did experience yet more fluctuations with my hormones...but cannot say for sure in what way. Is it progesterone going up?...is it estrogen dropping down?...is it the dynamic relationship between both?...are there even more hormones involved? I dunno. The endocrine system is extremely complex...AND amazing!!!
Anyway...the main purpose of my post was to let you know that I, too, experienced the constipation while using Iodine internally...and there are others that have posted the same experience.