You can try pulsing the Iodine (i.e. a pattern of skipping or decreasing the dose). That seems to help a lot of women having various problems with Iodine including me.
Here's some other ideas I'm using:
Try increasing your selenium intake as you increase iodine. I believe some of us are extremely vulnerable to H2O2 (Hydrogen-Peroxid) thyroid damage from high Iodine intake. We need to increase our Se intake to produce enough glutathione peroxidase to protect the thyroid. (I've also been through the constipation thing ..tons of water, Mg, vit C, herbals, fiber don't really do the trick except to give horrid gas, stomach aches and eventually diarrhea.)
Increase Se very gradually to watch for any problems. I would increase by 50 mcg increments. Ithyroid.com has an excellent explanation of why Se is needed with Iodine....go to the end of the selenium section for the authors take on this.)
Selenium can also help the detox pathways for heavy metals. The metals (and fluoride) can mess up the bowel neurotransmitter pathways. I believe those of us with sensitive neurotransmitters are the ones that get horribly bound up because of metal problems. High grade chlorella helps me. (Get a good quality that tests for metals in the waters - I'm using Prime chlorella from Canada.)
There is a second peristalsis pathway but it depends on shear bulk to get things moving. That's when stomach aches start as the bulk builds. In my case fiber makes it worse so I've learned to limit bulking agents and use enemas instead if nothing is happening. I'll also add in the coffee enemas for my liver. Coffee will increase the antioxidants as well ...particularly if you're using sawilson brand, but any organic coffee helps.
I also keep my b-vitamins very high especially b-12. I previously used injections but have switched to a liposomic b-complex (called AGE blocker). I think it works better than shots plus no prescription needed. High Bs will protect the neural pathways. Brewers yeast and molasses have Bs also.
This week started a liposomic glutathione after reading on the autistic sites how much it improved neural pathways by helping metal detox . Regular glutatione is degraded in the stomach. (Liposomics are mighty expensive so at this point the only only one I can say really works is the AGE blocker...i'll report later on the glutatione)
Iodine appears to make the bowels work so much better for the vast majority of people that those of us stopped up from it are a mystery to the rest. It can be so frustrating that we totally stop the iodine and give up. And we're likely ones that need it the most.