I suggest using the thyme, sage, parsley and just the tiniest bit of rosemary, as well as some of your other vegetables, both at the beginning and at the end. Put bunches of herbs in the soup (I tie mine into bundles using twine, so it's easier to fish them out) while the chicken is cooking. When it's done and your onions and carrots are mush, and your herbs are ragged-looking twigs, then strain the broth. I know that this is decadent, but just get rid of the mushy vegetables and the bundle of herbs. Then saute fresh onions and carrots and such add parsley, thyme and sage (if your broth doesn't already have enough!), and then add the strained broth and heat.
I'd also save a little dish of chopped herbs to sprinkle on at the table, too. Parsley would be best, but a bit of sage and fresh thyme would work. I'm hesitant about the rosemary, though, because it's so overpowering.