You are on the right track in terms of drawing the three best (non charged) resonance structures and using those to deduce bond length. I remember solving this exact problem a few months ago in my organic class.

At the moment I'm having trouble explaining exactly how to use these structures to precisely define relative bond lengths. Hopefully somebody else can chime in and explain.

If you were to draw EVERY possible charged resonance structure this method technically might work as well, but there are a near infinite number of those so this is obviously not the best method.