Bring 6 qt. of water to a boil over high heat in an 8-qt. stockpot. Remove neck and giblets from chicken. Add chicken, neck, and giblets to boiling water. Return to a boil, and cook 15 minutes. Cover, remove from heat, and let stand 20 minutes. Transfer chicken to a plate, reserving broth in stockpot; discard neck and giblets. Cover and chill chicken until cool enough to handle (about 30 minutes).
Meanwhile, combine tomatillos, next 3 ingredients, and 2 1/2 cups reserved broth in a medium saucepan. Bring to rolling boil over medium-high heat, and cook, stirring occasionally, 20 minutes or until garlic is very soft.
Skin, bone, and shred chicken, reserving bones, skin, and any juices. Cover and chill chicken until ready to use. Return skin, bones, and juices to broth in stockpot. Bring to a rolling boil over medium-high heat; cook 30 to 45 minutes or until the bones begin to separate. Pour mixture through a fine wire-mesh strainer into a large bowl, discarding solids. Return to pot. Skim fat from broth. Bring broth to a simmer over medium-high heat.
Process tomatillo mixture in a blender or food processor until smooth. Stir into broth. Add crushed tomatoes and next 3 ingredients, stirring until blended; bring to boil. Reduce heat to medium-low; cover and simmer, stirring occasionally, 1 hour.
Meanwhile, soak chiles in 1/2 cup hot water in a small bowl for 30 minutes. Drain, reserving soaking liquid. Process chiles and 2 to 3 Tbsp. soaking liquid in a blender or food processor until smooth.
Stir 2 tsp. salt and pepper to taste into broth. Pour chile mixture through a fine wire-mesh strainer into broth, discarding solids. Stir in shredded chicken, and simmer 15 minutes. Serve with lime wedges.