Some of my thoughts, as a somewhat educated former student of nutrition:
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Table salt may be iodized but I wouldn't necessarily look to it to be a good iodine source.
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Check your salt for other "filler" type ingredients. The one in my house has some unexpected non-salt ingredients (not iodine).
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Consider a less refined salt, but also look for iodine from other things besides salt.
I am personally using mostly Himalayan salt right now and I take an iodine supplement. I like using the salt grinder for a coarse grind.
This can be a pretty significant subject to delve into, but prolly good to do your own research.