The persistent DTC code 'Heater Booster' - Permanent, 9470, suggests that the heater booster itself might be malfunctioning. Common causes for your problem include a faulty heater booster unit, malfunctioning temperature sensors, or issues with the blend door actuators that regulate airflow between hot and cold. Even though you've replaced the valve under the wipers and checked all the fuses, these components could still be the culprits behind the random hot air from the rear vents. Using a good diagnostic scanner can really help pinpoint the exact issue. I've found that the youcanic scanner is quite user-friendly and excellent for DIY repairs, providing detailed fault codes and live data. Xentry is another powerful tool, though it can be more complex to use. Having a reliable scanner might help you diagnose the problem more accurately and get your climate control system back to normal. Hope this helps, and good luck resolving the issue!