I also found that. When i put focus into getting my arm movement right while running my breathing changed a surprising lot. It will go back to normal.
Stay patient. Whenever we are used to doing something one, and trying to change it, we will be a little inefficient. And, why your breathing is a challenge.
Be sure you are following the heart rate protocol and doing the drills and strength - they all work together to help with form.
The heart rate will help you keep effort easy, and in turn help with efficiency.
I have found the biggest challenge however, is to be patient and see this as a life long pursuit of mastery.