Waking up with high blood Sugar when going to bed with low (assuming you don't eat in your sleep) is called dawn phenomenon. That means your counter regulatory hormones are working well. No worries about that.
Eating fats will lower it, but you don't need to. FBG of 7 is no worry especially when fasting.
I don't know about your cortisol, but I lost 90 lb with or without the problem.
Cortisol is my suspicion only because I am tending to put on weight in the belly very quickly. I pretty much can fit 32 jeans onto my legs but cant button it up. Need a 36. Or after a 3 day fast, I am a 33.
Could be your condition - or not. But you need to get to the skinny side before you would have that problem. @ 10% BF, it matters.