How are your thumbs positioned? If they are not straight up, try that. That sometimes automatically brings the elbows in.
Did you grow up as a soccer player? I find that many soccer players run the way you describe. They have elbows out for protection and feet wide to help in changing direction. I had a girl whose feet were wide apart when she ran and she rocked from side to side. 20 minutes of working on it and consciousness during training cured it in a couple of weeks and she made significant gains in speed. Maybe you have structural or mobility issues, but maybe a little conscious work could make a big difference.