Perhaps a much smaller dose, and one that is cycled might be better for you.
LH is produced from the cyst formed when you ovulate. If you stop taking Iodine from the end of your menses until ovulation, then take your doses from ovulation throught to the last day of your menses.
The advantage of this would probably help you get and keep a pregnancy. No Iodine to change the way your system works up to ovulation, but the Iodine should help your body maintain progesterone levels from ovulation through conception and until the placenta grows enough to take over progesterone production.