Iodine and teeth/mouth health interested me to start with also.
I realise its not exactly the same but when i first discovered Lugols I placed a drop or 2 directly into a tooth cavity, inside it stained black and 1 year or so later one quarter of that tooth chipped away. I also used to do very dilute mouthwashes with Lugols in water and after a while I felt this bad and it made my teeth hurt like it does after drinking something acidic. I later found out that Lugols is acidic.
Im not contradicting what you're saying just thought I'd add my experiences.