In the past year, I almost always wake to 5.8 - 6.0....every single morning. I stay pretty LCHF etc and this will just not drop at waking..though I can get much consistently lower during the day.
Last week, wife was away so I thought the perfect opportunity to try some multi-day fasting...worked up to it and then did a 72 hour water/black coffee only fast (ended roughly Thursday noon).
Once I started, my blood glucose pretty well stayed solid at 5.3 the entire time (but still was higher the first two mornings) UNTIL I hit 48 hours fasting. Woke up to a 4.8, and it is like a switch turned on (or off). It was at that point my hunger pains went away etc as well.
I'm now back into some eating but only dinner every 24 hours (and a bit of heavy cream with coffee again in mornings), and very pleased with the numbers. Even AFTER some eating (including some carbs), I am not going above a 5.0.
So, just based on my experience....try a LONG water fast....it may change things. Still experimenting etc, but I will be taking fasting forward with me...