If you're sure there's insulin resistance, and you're already fasting and low carbing, then a HbA1c isn't going to be of much use. Maybe ask for an Oral Glucose Tolerance Test (OGTT)? Then they'd see the spike, if there is one, as it happens, and you wouldn't have to go through 3 months of carby eating to get the numbers corresponding with diabetes. No idea whether it'd be acceptable as a diagnostic tool in this case, but you could ask...