If they provide a meal then it should be OK, I think.
If not:
How about you have some snacks on your jacket pocket since they only go through your bags? You know, green tea bags, little sausage stick (pre packed, check for sugar content and nitrates), or jerky that has no added sugar, or a zip log bag of veggie sticks. It sounds silly, I know, they scan everything, but I am talking about small amounts not pounds of stuff.
What if you say they are needed for medical reasons? Such as insulin problems where you get sick and can pass out unless you have special snacks at certain time intervals? Would you need a doctor's note for that?
Another idea is to just look at their snack list and splurge on buying some stuff while on the plane.
You could also have a healthy meal right before going to the airport or before boarding and sleep most of the 12 hours and only have tea and water.
You might just have to take a day off induction and still stay below 20 carbs a day. You could have nuts as snacks, extra cheese or fruit and cheese platter/plate, low carb fruit (berries) or whatever they have to offer that is low carb.
I would still try and sneak something in my bag, just in case!
This is a tricky one!!!
I am curious what others will think of.
Good luck!