NO NEED TO BACKUP AND RESTORE FULL DATABASE. Differential will do...

1. FULL BACKUP;

2. Let One Log Backup and Restore on Secondary;

3. DISABLE Log BACKUP (DO NOT STOP LOG SHIPPING, DO NOT CHANGE RECOVERY MODEL);

4. Reindex;

5. Update Stats;

6. DUMP TRAN on Primary;

7. Differential Backup on Primary;

8. Copy and Restore Differential WITH NO RECOVERY/STAND BY on Secondary;

9. Start Backup Logs on Primary;

10. Copy and Start applying Logs on Secondary.