Hi, I've had half my thyroid removed as well (but that was more than 15 years ago) and I'm also hypo.
I tried Dukan for about 6 months last year and it worked for me as I lost a lot of weight (went from 150lbs to 130lbs), but then it was a bit too radical to keep at it long term because I love cheese and wine and can't stand low fat food :)
So I looked for alternatives and I found this one - more like a lifestyle than diet, but you could diet too on it: low carb, high fat.
www.dietdoctor.com/lchf
.... which is very similar to paleo.
The basic philosophy is very simple and sits well with my food 'beliefs':
^Eat: Meat, fish, eggs, vegetables growing above ground and natural fats (like butter).
Avoid: Sugar and starchy foods (like bread, pasta, rice and potatoes).^
Eat when you’re hungry until you are satisfied. It’s that simple. You do not need to count calories or weigh your food. And just forget about industrially produced low fat products.
Essentially what I've been doing lately is this: low starchy food, low sugar, normal/full fat stuff (natural fat as much as possible), regular protein. I feel fantastic and I'm able to maintain my weight with no effort really. It's become a lifestyle for me.
I follow this eating style very closely but not strictly - so I'll eat rice, bread, potatoes, etc once in a while but not daily. I try to get my sugar from fruit or honey if I feel like it, and I love dark chocolate.
Also, a couple of months ago I've stopped eating breakfast. I wasn't really eating much of it anyway and I read about intermittent fasting, so I thought why not give it a try. I do eat a bit more at lunchtime (12-1) and dinner time (6-8ish), and would have a snack in between if I feel like it. I try not to eat anything between 8pm 12noon the next day. It fits my lifestyle and I feel fantastic. I'm not doing intermittent fasting to lose weight, I do it because I think we eat too much, especially those of us who lead a somewhat sedentary lifestyle (9-5 office jobs...).
My thyroid has been stable for years now, with no change in hormone dosage.