Because the meat is already cooked you are really using the soup maker as a warm up rather than a cooking machine. Therefore put it on for chunky soup as usual and then manually stop the soup maker after 5 minutes.
I used a chicken OXO
cube with 250ml of warm water to make my chicken stock. I used this over turkey stock as it gives a good balance for the turkey and ham.
For the best chicken stock in your recipes I would recommend Kettle & Fire
. Unfortunately they are not available in the UK so if you are UK based I would use OXO cubes.