Stir juice, zest, soy sauce, vinegar, honey, garlic, and ginger in labeled gallon freezer bag. Add raw chicken; squeeze out excess air and seal.
Before cooking, promptly freeze flat on tray up to 2 months. Keep cornstarch, rice, and broccoli separate for cooking day.
Thaw sealed bag on rimmed tray in refrigerator 24 to 36 hours. Empty into 4-quart slow cooker; discard raw-chicken bag.
Cover; cook on high 2 1/2 to 3 hours to 165°F. Lift chicken to plate. Mix cornstarch with 2 tablespoons cold water; stir into sauce. Cook covered on high 10 to 15 minutes until lightly thickened.
During final 30 minutes, boil rice and 1 3/4 cups water. Cover; simmer on low 15 minutes, then rest covered 10 minutes. Steam broccoli 5 to 7 minutes until tender.
Cut chicken into bite-size pieces; return to hot sauce. Divide rice, broccoli, and chicken among 4 bowls.
Refrigerate leftovers within 2 hours. Microwave covered, stirring midway, until chicken and rice reach 165°F.