There's no curative diet for Graves'. You should be aware that having a diagnosis of one autoimmune disease puts you at greater risk of getting a second autoimmune disease, and some of those diseases have special diets. I wonder if that's why some people feel better on restrictive diets - maybe they have other issues that haven't been diagnosed.
If you go the RAI route, you may be asked to follow a low-iodine diet for a couple of weeks prior to the procedure. This means no seafood.
It's only temporary, though. On the thyroid cancer bulletin board (where I first learned about it) they say it's pretty bland. The reason behind the diet is to starve the thyroid of iodine so that it absorbs more of the radioactive iodine. I know cancer patients follow it, but I don't know if it's standard practice for Graves' patients. That would be something to ask your endo about.
Regarding blood tests, yes, you will have to have them for the rest of your life, but not as often as you do now. My endo told me that after my TT, once I was stable, I would only need labs and appointments twice a year. I have a tricky case and I'm still not stable yet, but I'm down to three appointments a year.
The risk of TED is greater with RAI, but you can still get it with TT. I have some very minor, intermittent issues in one eye. Like I said, I have a tricky case - low TSH that has persisted, and since my eye issue comes and goes, I'm hoping it will go for good once I'm euthyroid.