How did I do it? I came here, read a lot, read people's experiences, did some research on the listed thyroid Dr.'s websites, and took my health into my own hands.
You can do the same thing, don't be afraid to go up to a higher dose of iodine, and just dump those thyroid meds. I suggest you read as much as you can first, and get comfortable with taking the iodine. Maybe cut back the amt. of thyroid meds which is what I did until it's such a small amount that it's not noticable when you quit taking them.