Hi. I used to get very bad food cravings when I had more carbohydrates in my diet. I sometimes used to feel more hungry after a meal than I did before it! For me, I think it was all linked to insulin resistance and being sensitive to carbohydrates. If I eat a lot of vegetables, plenty of protein and hardly any grains or sugar then I don't get the cravings. For me it is something I always have to watch. I recently came across this anh-europe.org/ANH_Food4Hea...
which ties in with what I'd found worked for me many years ago.
I used to be a vegetarian and ate a lot of healthy-sounding carbs. They just weren't healthy for me.
I am also better if my meals are smaller - again I think this is linked to not over-stimulating the insulin response.
I realise this may not work for you, our bodies are all so different in the way they react to food, especially when the balance is being thrown out by medication, but thought I would mention it in case it worked.
I know what cravings can be like. One biscuit at a friend's house would make me feel ravenous to the point where I could think of nothing but going home and having my next meal. I'm now gluten, sugar and biscuit free and my life is so much easier.
If I do get cravings (and new thyroid meds have definitely caused me to have them) I eat things like raw vegetables. Or a boiled egg. It is not exciting....
Hope this may be of some use. You probably do this already, but worth a mention.