I totally understand. You must be killing off intestinal cooties too. You don't want to get an electrolyte imbalance from mineral loss through the bowels. You may need to pulse your Iodine dosing, on a day, off a day. Dr. Brownstein pointed out that some people cannot take Iodine every day.
Regarding the stomach upset. Have you tried using Iodoral? It's easier on the stomach. You could start by breaking one tablet in half?