As I understand it when we eat carbohydrates our body uses the resulting glucose for energy.
In the absence of carbohydrates our bodies will make ketones from fat and uses those ketones for energy.
So if the level of carbohydrates in your diet is low enough, your body's only option is to use fat by changing it into ketones.
The only way you can lose weight is to use your fat for Energy by producing ketones, so when you lost your weight you must have been in ketosis no matter what your fasting level was.
Fasting levels or the dawn phenomenon is caused by the liver releasing stored glucose or making new glucose because it thinks you need it.
I don't think there is a solution, livers do the job they have evolved to do, our problem is not the liver doing what it is supposed to, it's not being able to process the resulting glucose efficiently.
By not continually topping up our glucose stores through eating more carbs than we can handle, hopefully our fasting levels will improve.