Of course there are many possible contributors to weight gain. After diet and exercise, one of the ones that needs to be considered is low metabolism. It is amazing how much a metabolism that is even 5 or 10 % lower than normal for your age, weight and height can affect your weight. Have you been tested for your thyroid hormone levels? If so, please post results and reference ranges. If not, then you should try to get tested for TSH, Free T3, and Free T4. Note that the latter are not the same as Total T3 and Total T4). If Free T3 and Free T4 are in the lower half of the so-called 'normal' range, it is frequently associated with being hypothyroid, with associated low metabolism.
Yeah I have had a liposuction long back. It worked well for me. It could remove the excess skin and fat deposited at my abdominal portion. I think it is one among the good decisions that I took in my life because it could make me feel confident about my body. I got it done from Steels Avenue Cosmetic Clinic at Toronto. Dr. Robert Backstein was my surgeon.
But in your case, I am not sure whether you can undergo a lipo. I wasn't a Hashimoto's patient and I never had any health issues other than back pain.
So it would be better if you ask a surgeon directly, rather than waiting to get answers from this forum. I think you need to get consulted in the first place.
One of the prime symptoms of hypothyroidism is puffiness of the face; are you sure your thyroid hormone levels are where they need to be? If you have your latest lab results, feel free to post them, with reference ranges. It could be that you simply need an increase in your dosage.
I'm not sure why you dubbed synthroid and liothyronine as "evil and disgusting". Many of us, on this forum, are on some form of synthetic T4/T3 and are doing just fine. I actually prefer it, so I can adjust each med, individually, as needed.
The matter of liposuction is one that you would have to take up with your doctor to make sure it's right/safe for you. I don't know of anyone on this forum who has had liposuction or who is contemplating it, at this time.