In general, for the doses of iodine we talk about, Lugol's, SSKI, Iodoral are used. Some have used Iosol, Magnascent, Detoxified. Kelp usually would only be useful for smaller dosing, maybe up to 1 mg iodine. You might or might not be able to reduce your desiccated thyroid. We look at iodine being used throughout the body, not just the thyroid.
Check out the "Answers" (FAQs) at the top of the forum. Here are two sites that might get you started. I included a video lecture given by Dr. Brownstein, because I like visual aids.