Reserve chicken breast from the cut up chicken.
Place the remaining pieces in a large pan with the pork hock and water.
Bring to a boil, skim off any foam, then reduce heat and simmer, covered,for 2 hours.
Add all the chicken breasts and continue simmering for 25 minutes.
Pour broth through a colander and reserve the pieces of chicken breast.
Discard the remaining residue.
When chicken breasts are cool enough to handle, remove meat from the bone, then skin, and cut in bite-size pieces.
At this point you can refrigerate chicken meat and broth up to two days.
Cover mushrooms with warm water and let stand for 30 minutes.
In a separate bowl, cover tangerine peel with warm water and let stand for 30 minutes.
Drain mushrooms, cut off and discard stems, squeeze mushrooms dry, and thinly slice.
Drain tangerine peel and scrape off inside of peel.
Trim fat off ham and dice the lean meat.
Cut top off melon and reserve; scoop out seeds and stringy portions.
Place mushrooms inside of melon along with whole tangerine peel, ham, ginger, water chestnuts, bamboo shoots, and lotus seeds.
Skim fat off chicken broth.
Reheat broth and season with sherry, sugar, and salt and pepper to taste.
Set melon in a bowl, then set bowl in middle of a dishtowel and lower into the cooking pan with the rack in the bottom.
Pour broth inside melon to fill it three-fourths full.
Put top on melon, add enough water to pan to reach bottom of steaming rack.
Cover pan and steam over low heat until melon meat is tender (about 3 to 4 hours).
Replenish water in bottom of pan as it evaporates.
Just before removing soup from heat, add the pieces of cooked chicken breast.
Lift melon out of pan; remove and discard tangerine peel and ginger.
Spoon some of the soft flesh inside the melon into each bowl when you serve