I do think that eating fats and proteins is better at curbing hunger than just reducing calories while including high-carb foods. Maybe that is related to the insulin effects you mention.

But, as an example, I would go to In-N-Out and order a double-double protein style. It is very low carb, and it is kinda cool that you can pretty much eat a hamburger on "a diet."

But think about how big a change that is just from a calorie perspective. I would have gotten a bun and fries before and included carb-y toppings like ketchup. It's a huge reduction in the amount of food I was eating and eliminated the most calorie-dense foods, too. I am an advocate for low-carb, but I think it might just be an effective way to reduce your total calorie intake.