Just a note, SJ...while I wouldn't impose on your current recipe, I would ask that you assure a 1:1 ratio in volume of chicken to water. Additionally, if you have the whole carcass then remove the wings, thighs and drumsticks from the carcass and with a mallet used for tenerizing steaks break some of the bones... excellent for flavor and adding, as already mentioned, appropriate gelatinous consitency for flavor.
Additionally, we like to put the pieces and parts in a foil lined baking pan and place it under a broiler in our oven for about 30 to 40 minutes until they are nicely browned... adds a great note to the flavor. We also like several sprigs of fresh Rosemary to round it off, but I recognize that's a preference not shared by all.
Lastly, in your next go at cultivating stock, see if your Vietnamese friend could save you 4 chicken feet. They like to use them in many dishes and we have an Oriental friend like that that said they really do wonders for the stock as far as flavor and getting just the right texture. They're cleaned and ready to go right in the pot. Just pour everything through a colander before storing... (takes out the tough toe nails, dontch'a know?).
Best of luck!