I know 2 folk who after cutting out all dairy products completely have 95% cut out their migraine issues. Perhaps this is an experiment you have done or willing to try? I don't consume any dairy whatsoever and haven't for 3 and a half years and haven't suffered any headaches or migraines myself, apart from the odd hangover which is indeed very rare I'll drink that much.
A Different approach works for different folks, as LissaJous mentions about she eats lots of fat and protein, my personal eating plan is high carb with very little fat and protein intake and it works wonders for me. The dairy though could be a big fact, especially as vegetarians seem to eat lots of it I have found. (Not assuming you do.)
Consistent hydration 24/7 365 is of course essential.
Hope that is 'food' for thought