A 28-year-old multiparous woman from rural Maharashtra attends the primary health centre for family planning counselling. She has completed her family (2 children, both healthy) and wishes to avoid pregnancy for at least 5 years. She is breastfeeding her 6-month-old infant and reports irregular menstrual cycles. Her husband is supportive of any method. On examination, she is healthy with no contraindications to hormonal methods. Which contraceptive method would provide the longest duration of protection with the highest efficacy and minimal impact on breastfeeding in her current situation?