I was exactly the same, until a year ago I started to eat to my meter, and became low carb. Then I started to go underweight, so gradually increased my fat. Now I eat all the natural fat I can. Double cream, fatty meats, coconut oil..... Your taste buds change / acclimatise. My diet for last 6months is around 5%carb (36g), 15% protein and 80% fat. My calorie intake is around 3,500, any less and I loose weight. 6'-2" BMI 22. Hba1c 5.1%.
Worried what it might be doing cholesterol wise etc. I asked my Dr for a blood / health check. Dr and diabetic dietician say all is very good and are now supporting me with my LcHf diet... Dietician says it all goes against her training, but my results are the same as another LcHf patient.