@Tim65, your early morning highs may also be enhanced by rebound as the liver dumps glucose overnight to counter the low you experience.
I've found that Dawn Phenomenon is much worse when I eat carbs pretty much after 6pm, so I've basically stopped doing that. It makes a huge difference to me. I don't find that exercise makes a huge amount of difference.
On your Levemir - do you take two doses? 2u before bed is a tiny amount. If that is all you are taking, you could move it to the morning so that you don't get lows overnight and are better positioned to monitor what is happening during the day.