exercise timing to lower morning fasting levels?

It is important to understand the effect of exercise on blood glucose.
when you exercise the activity acts in a similar way as the insulin your are taking.
Speak to your diabetes health care provider and discuss the exercise program you are doing, take with you the records from your daily testing and he will make the necessary adjustment to your dosage to avoid some of your concerns.
the most important thing here is that you are exercising and it is a matter of preference as long as you have a proper diabetic diet.