Season both cuts of chicken with the salt, cumin, garlic powder and lime zest.
Arrange the chicken in a 6-quart slow cooker and add the broth, honey and 2 tablespoons lime juice.
Cover and cook on low until the breasts and thighs reach at least 165°F, 4 to 4 1/2 hours.
Move the chicken to a rimmed pan and shred it into thick strands.
Skim the cooker liquid and stir in the remaining fresh lime juice.
Fold enough of the lime cooking juice into the chicken to moisten it before serving or cooling in portions.