Remove the neck and giblets from chicken. Place chicken, breast side down, on a cutting board. Use kitchen shears to make a lengthwise down one side of the backbone, starting from the neck end. Repeat the lengthwise cut on the opposite side of the backbone. Remove and discard the backbone. Turn chicken cut side down. Flatten the chicken as much as possible with your hands. Use kitchen shears to remove the wing tips.
For marinade, in a bowl combine orange juice, lemon juice, olive oil, snipped parsley, garlic powder, onion powder, pepper, and salt.
Place chicken in a resealable plastic bag set in a large shallow dish. Pour the marinade over chicken. Seal bag; turn to coat chicken. Marinate in the refrigerator for at least 2 hours and up to 4 hours, turning the bag occasionally. Drain chicken, discarding marinade. Pat chicken dry with paper towels.
Starting at the neck on one side of the breast, slip your fingers between skin and meat, loosening skin as you work downward. Free the skin around the thigh. Repeat on the other side. Spread Citrus Rub all over and under the skin of the chicken with fingers.
For a charcoal grill, arrange medium-hot coals around a drip pan. Test for medium heat above pan. Place chicken, breast side down, on grill rack over drip pan. Weight with two foil-wrapped bricks or a large cast-iron skillet. Grill chicken for 30 minutes.
Turn chicken bone side down on rack, weighting again with bricks or skillet. Continue to cook, covered, about 20 minutes more or until chicken is no longer pink (180 degrees F in thigh muscle). Add orange wedges to grill the last 10 minutes of grilling time. (For a gas grill, preheat grill. Reduce heat to medium. Place chicken on grill rack over heat. Cover; grill as above.)
Squeeze orange wedges over chicken. If desired, garnish with parsley sprigs.
In a small bowl combine olive oil, finely shredded orange and/or lemon peel, parsley, honey, kosher salt, and ground black pepper.