Well, it depends what you mean by 'diet' and 'eating what you like'. If eating what you like is stuffing yourself with sugary cakes and chocolate, you probably couldn't do that without consequence. But the odd iced bun wouldn't hurt - unless you're Coeliac. And, if you mean by diet, low calorie, then you shouldn't be doing that, anyway. You should be eating your fill, but of good, clean food. To a certain extent, I do now eat what I want, but I don't want very much. I don't know how it would work out if I had a large appetite. But, I never approve of calorie-counting.
And, of course, it does depend what your hypo weight consists of. Is it really fat? Or is it water weight? If it's water weight, then no amount of diet and exercise is going to shift it, anyway. It's all down to keeping your FT3 level stable. Too low, and the water (mucin) will return. Too much and the mucin could still return. If it's real fat, then low-calorie will make things worse, so you do need to eat a reasonably high level of calories, to maintain conversion. As you say you can put on weight just by drinking water - which doesn't surprise me at all - then your problem is probably mucin. Fat does not accumulate rapidly. Putting on real fat is a long, slow process. Retaining water can be almost instant.
The odds are, you will always need certain supplements - yes, I know that bugs you. It bugs me, too. So, now that I think my levels are pretty good, I have little holidays from them. But, at the slightest twinge, I start again. You are always going to have to stay in touch with your body, that's for sure. But, it becomes second nature, after a while.