I got to be realy honest here. ....WHY, are you focusing on just average programs as you call them. I am certain and would hope that if you are committed to a specific area, and the field of EM that you will apply to ALL the programs that are in the Chicago and Greater Chicago area. I did my fellowship at Christ and am familiar with several of the CHi-town programs.
A few thoughts:
Obviously consider rotations at one or 2 of the programs that you may think are more competative. RE: if they are more competative they are liekly to challenge you more and you want to show folks that you not only can handle it, but will thrive on it! Also many students have literally moved up in the match due to their rotation performance, and leaped over "high number" applicants. Be willing and ready to turn heads during the rotation...be a gunner...not cut-throat..just a solid team player willing to go the extra mile, let your performance get you rfecognition. I am telling you that news of residents and students who are like this travels faster than Isabel's wind speeds! Just today as I was walking in, and a partner stopped me to mention a med stud who was awesome and a joy to work with, hard working, thorough, inquiring, and a self starter. repaeted the student's name, medical school and future EM interests! You make a strong impression on a rotation you will ROCK regardless of what some numerical performance metric scale says! understand many letters of Rec are stndardized, but you occasionally get a real thought out letter from the heart about a student that makes you want to meet them regardless of what the numbers say.
Rotating at a program often will get you an interview as a recognition of your time and effort, regardless of numbers. You should be able to ask.
Also there is a bidding concept that does occur. If you get strong letters from a competative program this does get noticed and highlighted for most programs.
So good luck, and do't sell yourself short...ever!
Paul