Keep limiting your carb intake. Get enough protein (your body should tell you), and then eat enough fat to satisfy your hunger.
The body’s energy sources are glucose and fatty acids. Our metabolism is either in glucose-burning mode or in fat-burning mode, depending on the level of insulin. If it’s high, we metabolise glucose (partly to simply get rid of it; too much is toxic), if it’s low, fatty acids. While glucose/carbohydrate is a strong stimulus for insulin production, fat triggers it very little, no more than the bare amount needed for survival. Fat also metabolises without the damage caused by glycation. So, in many respects, it is a safe, clean fuel to be burning. As Jason Fung, likes to say, “To burn sugar, eat carbohydrate; to burn fat, eat fat.”
We recommend 1.0-1.5 g of protein per kg of lean body mass. Some experts recommend up to 2.0 g/kg. This is a tricky subject, and people’s need for protein is individual. If you’re not getting enough protein, you are going to feel unsatisfied, no matter how much fat you eat. So start in the recommended range, and adjust from there, would be my advice. And remember (some people forget this) that meat is only about 1/4 protein, so to get 100 g a day of protein, you need to eat 400 g (about 14 oz.) of meat.