Digestive enzymes helped me too when I had IBS; not Iodine related as I had it for a couple of decades. Now I dont need them anymore.
What helped more than anything for me was vitamin B`s and some zinc. These are good companions for the iodine.
Vit B, zinc, magnesium needed for most enzyme reactions in the body. Also for strengthening (lowering) the stomach acid; if this has too high PH, it will ferment the food instead of ingesting it = gas.
The leaky gut because of proteins that aren't properly digested caused by the weak stomach acid. Iodine is one of the things needed for it, but dosage may matter.