all things in moderation.... don't over indulge and see what benefits or issues you can have.
I agree with the Red also on looking into the supplements she suggested along with Vit C - Vit D and zinc/copper with the magnesium.
Well, if you eat them all in one day and every day, you aren't going to get better!
Iodine is high in many of the foods you list and you really don't want to over do it. You will end up with a hyper thyroid and more problems than you need.
It's perfectly ok to have these things occasionally, not every day. Our bodies do need a small amount of iodine. I would certainly make sure you keep the kelp intake well down.
Eating healthily will be a better way to keep your body in tone to help fight the thyroid disease. In 90% of the world our iodine intake is sufficient to allow our thyroids to function with no extra being needed. If you live high in the mountains and grow your own food, then you might need a supplement of it, but I doubt that is in your case.
Depending on your condition, your Synthroid may not be adequate, and might need to be re-evaluated.
Don't go self helping with the iodine, try using selenium and magnesium supplements instead. These are needed to help the thyroid medication do its job properly.