Well, I had a problem with waking at 4am, overheated. If that happened, my blood glucose would also be high when I finally got up (around 6-7am) at 100-105.
I know this sounds crazy to a lot of low-carbers, but I added sweet potatoes and fruit to my diet. Not a ton of it - I eat about 20-25g per meal (about the same as I eat in protein per meal) and it stopped happening. Morning BG is now 85-95, and I don't wake up at freakin' 4am either. I wind up eating less over all, but I seem to do fine with less protein now.
My theory is that it was too taxing for my adrenals to get the BG out of protein after years of low-carbing (which I did before I was paleo). I know I have not felt this good for a long time. I used to eat more like 1.5 lbs. of protein a day, now I eat more like 13-15oz. I still eat lots of green vegetables, and my total carbs daily are around 100g.