I looked into this further, but the original assessment was correct. Even if we tried to handle synchronous errors, we can't reliably classify this error as a bounce because the response code and message are too ambiguous and list several possible causes.
The message appears to come from Exim, which is used by cPanel/WHM. You may want to ask your hosting provider or server administrator to check the Exim logs and DNS/routing for an affected address, and see whether the server can accept the message and send a more specific bounce to the bounce inbox instead.