I have recently come across two friends who have had cats diagnosed with thyroid problems by the vet, both animals were put on the medication your describe at great expense. Both cats developed nasty lesions on their body and one of them was really miserable as she had to wear a collar to stop her licking them & making the lesions worse.
One friend was recommended to take her cat off the medication & feed her special food which she buys on the Internet. As the drugs were costing a lot (plus the vet consultation fee every visit) she decided to go with it and the cat hasn't looked back. I told my other friend about this too and put her cat on the same food, stopped the drugs and again, cat is happy, healthy, eating and the nasty sores on her neck are disappearing. Apparently it's the iodine in ordinary cat food that makes some cats ill, this other cat food doesn't have it in. You aren't able to feed them anything else though, no treats, chicken, fish etc but its got to be worth a try?
For the life of me I can't remember the name of this food but it is available from vets (costs more) but also from amazon (a lot cheaper). If you a) ask your vet I'm sure they will tell you the brand name or b) search online, I'm sure it will come up. Let me know if you can't find it and ill contact my buddies for the name.