Remove and discard giblets and necks from hens. Rinse hens under cold running water; drain well and pat dry. Combine 1/3 cup soy sauce, jam and nutmeg; brush cavities of hens thoroughly with mixture.
Coat rice with 4 teaspoons soy sauce. Stir in apricots, pecans and green onions. Stuff hens equally with rice mixture. Place hens, breast side up, on rack in shallow foil-lined baking pan; brush skins lightly with sauce.
Bake in 375 degrees F oven 45 minutes. Brush hens thoroughly with sauce; cover loosely with foil. Bake 45 minutes longer, or until hens are tender; brush occasionally with remaining sauce.