The early morning highs might have a physiologic reason: around 3 am everyone has a low and then the liver starts to release the emergency stash of glucose so that we have enough energy for the morning. It's a mechanism that works in every mammal, wether healthy or diabetic. It's a natural failsafe against critical lows. The time it starts varies depending on when the suger in your blood is used up. So if you have a late evening snack, it can start later than the average 3 am.
So your high in the morning shows that your liver does its job properly =)
Also, there are 2 different types: in about 60% of all humans the cells take up glucose better in the morning. In about 40% they work better in the evening. I'm an evening type and frequently have highs until about 10 am, since the liver-released sugar stays in my blood so long, what with my cells still being in sleep-mode, so to speak. Perhaps you are an evening type, too?