What do your glucose numbers look like?
On average e.g. do they swing from high to low or do they remain steady? Do you take them before and after you eat?
Knowing that information would most likely explain the source of your headaches! i.e. your personal threshold for tolerating lower blood glucose which in turn if they are too low can cause headaches because your still adapting to lower external glucose intake verses your liver producing enough glucose to sustain your brain as the ketones that are floating around in your blood (if they are real high?) are not really (partially) being used by the brain yet for fuel?
Eating a little bit of protein at the onset of the headache might relieve it!