Heidi, have you considered that you may actually need to lower your basal rate? 

As you know, exercise reduces the need for insulin.  The effect lasts for 24 - 48 hours (or thereabouts) although in my case, it seems to diminish by the second day unless I continue my daily exercising.  Given that, is it possible that you are dropping too low during the night and your body is (over)compensating by dumping glucose from the liver into your system? 

It's only one possible cause for your high morning bg, but you might want to test a couple of times during the night and see if you are going too low, then too high, as you sleep.  If you are a pumper (and if necessary), you could adjust your rate downward for those hours. It's been a long time since I was on MDI, so I don't know what to suggest if you inject.  A small adjustment to your basal dose might be helpful. 

I understand your frustration with trying to exercise while having to take diabetes and insulin into consideration.  For me, it's not just the corrections needed for exercise, it's the corrections needed when I start losing weight because of the exercise.  There are so many times I simply want to give up because it's so much trouble and so ongoing because the more weight I lose, the more adjustments I need.  Sometimes I think that exercising and losing weight would be so easy if only I didn't have diabetes.  While I realize that both are not easy for anybody, the diabetes is the frustrating factor that most often makes me want to give up.

Having said that, this time I am committed to continue as I have had some non-diabetes health issues come up.  I consider it imperative to continue exercising, so I will.  I trust you will, too.  Hang in there!

Jak