I know you are interested in schools that do not interview but, the interview can help you. Typically if you apply to a school that doesn't interview you better have really strong GRE/pre-reqs/reference letters because that is what they will base their admissions on (ie. UW-La Crosse, average pre-req gpa this year was 3.8, GRE of 1200).
The schools that interview could accept someone that do not have as great of pre-reqs/grades if they feel that person has the potential to be successful in the field