Yes I do get it. You say you don't lose weight on a low carb diet, but you haven't checked how many carbs you have a day. Surely that's important? If your own personal carb tolerance level is, say 20g daily, and you have 25g, then you won't lose weight, regardless of total calorie intake.
What you call the 'hunter' gene is what I call the 'thrifty' gene. If there was a famine you and I would survive longer than most because our bodies can live on fewer calories than most people, so we don't lose weight easily.
It doesn't matter what fancy label you give yourself. If you are insulin resistant (for whatever reason) then you need to limit carbs to below your own personal tolerance level and also keep an eye on protein. Exercise is good too, but is secondary to strict carb counting IMO.
I am not sure why you are worried about 'changing sugar into fat'? As
@4ratbags says, if you are on a very low carb diet, then you won't be having any sugar, just like a lot of T2s on this site.