well I have always been a little like this - overweight, HANGRY and very low energy when in need of food, put on weight super easily compared with similarly active friends with much worse diets.
The last time I went low carb about a decade ago, it really did help smooth out the hunger pangs and I did lose some weight on it.
Would like to have a long oral glucose test where they test out the insulin response. Will see if doc agrees next month.