You make some very good points, I like your reasoning skills.
"Then I started working on re-mineralization. I have found that this has solved most of my problems."
That is a powerful statement and brings to light the very real need for balance in all things, including iodine.
Calcium fluoride is found in bones and has been shown to be essential in the hardening of the enamel of teeth. That said, these studies from over 100 years ago were dealing with fluoride consumed in foods etc. along with the accompanying calcium and ALL additional co-factors... NOT industrially produced fluoride waste.
This makes a huge difference. I also believe that bromide has its roles in the body as well... it is all a balancing act that has been thrown out of balance due to many different reasons.
Halide balancing is important... I will avoid unnatural forms of halides and not worry a bit about those, including bromine and fluorine found in foods.
I do not think it uncommon at all to find an individual that can benefit from a nutrient and another that needs to limit exposure in the same house. I see it all the time.
As an aside, I have put as much as 40 drops of Lugol's in coconut oil and rubbed it all in over my body... no apparent affect at all.