Hi
@Swiggy, Firstly a big hug for trying to get a handle on your diabetes control. Your c-peptide does suggest a high degree of insulin resistance, so your pancreas may be pouring out very high levels of insulin even to address a small carb load - this will encourage your body to store fat, so fat loss will still be a challenge. But good news you are still able to produce high levels of your own insulin. You are NOT a failure. This is a metabolic disease that can be incredibly difficult to manage, but almost every diabetic can improve their control through active management.
Great that your GP supports low carb. Have you checked out dietdoctor.com for really yummy recipes? If your gut tolerates it, metformin is a really helpful drug that may have additional helpful effects re inflammation and cancer suppression. Plus any additional exercise you that can tolerate, even small increments in walking, can really help stabilise BG levels and importantly boost mental mood.