I’m not sure why you should still be on tapazole five months after RAI. I hope you are actually looking at your blood tests as they come in so that you, too, can see whether or not you are "almost normal" or not. I wouldn’t expect an endo to misread blood tests, but my GP did in fact misread mine, so it’s a thought.
As to weight gain after treatments like RAI/surgery, etc. hyper levels of thyroid hormone remove muscle, and the muscle does come back slowly after we normalize our thyroid levels. Muscle weighs more than flab, but it occupies less space typically. So, a better gauge of your weight issue is not the absolute number on the scale, but how your clothes are fitting. If you are regaining muscle you WILL be gaining weight. And especially since you have been working out so frequently you should be seeing muscle rather than flab for the most part. I did regain 25 of my lost pounds without changing clothing size.