I'm the same as you. Fasting sugars are higher than my target (above 7 mmol/L) 3 out of 5 mornings. Frustrating! The rest of the day my levels are just great. I have a bad case of DP.
I'm seeing the doc again in 2 weeks, perhaps medication will be increased at night. Don't know yet! I've tried everything, from not eating supper (very bad idea, made it much worse!! 11.5 mmol/L in the morning) to eating veggies and a lean meat, no carbs at all. Nothing seems to work. My body has a mind of its own.
Talk to your doc!
The very best to you.