A better way would be to go through the normal filtering process of accepting applications. Choose several designers, then offer them this same task with proper payment for their time.
The idea this is unfair or "spec" work seems silly to me. As a professional, you do a ton of stuff that you don't get paid for: attending classes, building your skillset, designing your portfolio, writing your resume, creating concepts, etc., etc. This is simply a fact of life.