Many medical schools with EDP have requirements (or suggestions) that potential applicants contact the admissions committee before applying EDP.
You have good stats and a publication, but I see very little nonclinical volunteering. What are your hours like for that?
With well written essays and a clearly communicated goal for medicine, you could get in somewhere, or you could get in nowhere. Your chance is 74% based on AMCAS data for students with your MCAT/GPA.
In your position, I wouldn't apply EDP unless you get strong encouragement from the admissions committee to do so. You stand a decent chance of getting into your state school even if you apply normally, so I don't see the benefit of limiting yourself to one school and disadvantaging yourself at others.