I've been a member here for a while, but haven't posted much. But just had to share this idea.
Its a long story, but I gave up sugar about a month ago, and then gradually reduced all my carb intake until I am now eating low carb/high fat, and consuming well under 30 grams of carbohydrates a day. I've done it as a way of losing weight I gained when I had to come off thyroid medication for a while, and it is working well for that.
I've joined a few facebook groups on low carb eating, and migraines have come up as a topic for discussion a few times. Lots and lots of people are saying that either cutting out sugar, or going low carb, or even ketogenic (very restricted carbs and high fat) has cured, or at least reduced their migraines. There was one story of a 7 year old girl totally crippled by her migraines completely cured by giving up sugar.
In my case I haven't had a migraine since I started this journey. And as a result of the diet change I rarely feel hungry enough to bother eating until mid afternoon. In the past just missing breakfast would have set off a migraine, so something has really changed around here!