Psyllium husk as gelatin replacement.

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.

I'd place a tray in my sink a slowly run water through it, then sit the jelly on top of the tray, such that the bottom half of the jelly mould is under water. The constant, gentle, flow of cold water will cool the jelly quickly.