Add gelatin to soup as a replacement for stock?
I'm looking for the online reference, but I remember reading in Cook's Illustrated that they were able to substitute a bit of gelatin to mimic the mouth-feel of homemade stock. I did find a beef stew recipe that used gelatin. 

Based on how you described your recipe, I would say that the long cooking of chicken bones is indeed what's missing. You might get a better result if you roast your chicken breasts and vegetables before cooking them in the broth.