One method of fasting to reduce insulin insensitivity is to limit your eating to a few hours a day, so just have one meal with water in between, or have two meals within a few hours of each other (breakfast and lunch) with no other food in the day. (I would add at least a packet of salad to the eggs and cheese and have oily fish instead of cheese some days.)
Remember you are not trying to lower BG with a fast, you are trying to increase insulin sensitivity, so it is the BG readings (before/after meals) after the fast is over that shows if it is working.
But check your meds carefully before doing any fasting, as some meds will result in a BG that is too low if you skip meals.