I'm not sure the cord blood or TSH values are appopriate predictors of fetal health in the presence of iodine. Notice they did not follow the actual child.
All I can say is that if it were my baby, and I hadn't taken Iodine before, I would alsolutely be taking low dose Iodine AND progesterone.
The reason I say "low dose" Iodine is not to expose the baby to any possible detox. But that is just a theoretical possibility.