I'm not sure about the specifics of your hormonal situation, but I will say that I also feel that Iodine disrupts my hormones. My menstrual cycle was always like clockwork for my whole adult life. Exactly 28 days every month. When I started taking Iodine (about 30-40 mg per day in the form of Lugols), my periods became irregular and were frequently late. Since then, I've had to back off on the iodine, but even just a few drops a day has this effect on me, so I'm now down to 1 drop every few days, and will see if my period comes late this month. (About 6 months ago I simply quit the Iodine altogether for a few months, and my periods went back to being exactly 28 days, then when I went back on the iodine, even at a smaller dose, they were irregular again, so I know it's the iodine that's causing me to be irregular.)
I also have gained 10 pounds in the last year and apparently have a "thickened endometrial stripe," (thickened uterine tissue) which we are just watching at this point, and not doing anything about. I have no clue if the iodine played a role in the weight gain and uterine issue, but it's not out of the question, since it obviously affects my hormones and female organs. I'm hoping these two issues resolve on their own, now that I'm taking very little iodine.
I wish I could offer you some helpful input, but all I can say, is follow your gut and if you think iodine is disrupting your hormones, maybe it is.