Sorry I'm a bit late to the party today!
Tee, I am a type II diabetic and, like you, until my daughter was born was able to control my diabetes through tablets and diet (eg everything in moderation, following standard nutritional advice given etc...). As soon as I got pregnant I had to go onto insulin to control it and it seems to have caused permanent damage to my pancreas as since having her my diabetes has been much, much harder to control. Eating what I ate before having her simply didn't work for me, and like you my hba1c kept creeping up.
I fell pregnant again about 18 months ago, and had to go straight back on the insulin. I had a mc, but my diabetic team have kept me on insulin so that I can continue to ttc and keep my levels tightly controlled. Obviously being able to test all the time (for free!) has allowed me to really get to grips with what foods have what affect on my and my blood sugars. If I follow the official advice (eg porridge for breakfast) then if I don't take insulin my blood sugars go sky high, if I take the insulin required to keep them just below the 8 level two hours later, then 3 hour later I have a hypo or have to eat something else to prevent this from happening. A similar thing was occuring every meal, the only way I could manage it without having to eat extra to prevent the hypos and keep my blood sugar levels within target was to cut out the carbs.
I talked to my diabetic team about this and they were a little unsure, although only because they were worried that I wouldn't have enough energy to get from one meal the next and then would snack and then eat more/put on more weight etc... I have agreed to have my bloods done/be reviewed as regularly as they wanted. I have kept food diaries and shown them and actually what has become apparent to me is that I eat much better following a low carb regime. I no longer require any insulin at all during the day time and only require my background insulin at night and at a much lower dose than I had before. Over the last 12 months, every single one of my blood results has improved and my hab1c is now well within target, my cholesterol has come down and I have also lost weight. I never feel tired, I never get the three hour slump after a meal and I am eating foods that I enjoy. I read Dr Bernsteins 'The Diabetes Diet' which I also found helpful from a diabetic point of view.
I am surprised to hear that you get migraines when low carbing - this goes against everything that I have read and must be very unusual. Refined carbs are a well known trigger, and many people have found cutting out carbs has helped. I know that some people if they don't eat enough vegetables or variety of vegetables can then lack some nutrients which can cause migraines so taking vitamin/supplements (B12 and another one I can't remember) is recommended.
I think there is a common misconception between 'no-carb' and 'low-carb'. I do eat carbs, they all just come from natural sources - vegetables (excl potatoes). I know from extensively testing my blood sugars that actually eating a plateful of carrots is much better tolerated by my body than eating even a small portion of rice or slice of bread, despite there being perhaps a similar amount of carbs when compared.
In terms of breakfast others have already suggested things to but: scrambled eggs, boiled eggs (these can be done the night before), bacon, low carb sausages (again these can be cooked the night before and warmed in microwave to save time), breakfast muffin/frittata things are great (again can be cooked before), cooked mushrooms, cold meats and cheeses or any combo of the above. For me a typical day's meals would go:
B - bacon/eggs/mushrooms (I try to get up early to make time for this as it makes a difference to me)
L - salad with some kind of topping (prawn, avocado, meats, cheeses, egg mayo, goats cheese, whatever they have on special offer in the shop!)
D - meat/fish with a couple of veg (green beans, broccoli, cauliflower, salad, cabbage, leeks, courgette)
I also drink about 4 litres of water a day
I know you say you have spoken to lots of nutritionists about this, but they are only going to go on what they have been taught if that makes sense. Anyway, that is my personal experience and honestly think that this WoE has been the best thing I have ever done for my health and diabetes.
Sorry this is such an essay!