I'm NO EXPERT so take what you will and leave the rest. My suspicion is the gum deterioration isn't connected with iodine. Mine got worse when my stress levels got acute: direct cause and effect. What exactly causes this should be left to someone with command of biology but, figure it's tied into adrenal response: cortisol. Only just begun Iodine supplementation and it's been a rocky start but, it's getting better the past few days.
You might consider oil pulling which I've read people have healed their gums, brightened their teeth and relieved bad breath from pulling. Have even read where one poster said they give a tbls to their dog ever day and their teeth are brighter, doggie breath is gone and gums are excellent.