Been there, done that too. Government bureaucracy, corporate bureaucracy, same diff.
Sometimes you have to get pretty clever in order to outwit that automated phone system. One time I needed to call my former corporate employer about my retirement account. The automated message didn't give me any clue about how to reach an actual person in that department.
So I called another department, and the person there told me they make it difficult to get through, on purpose. She told me, "when they give you the prompts to choose from, just start pressing numbers. The system will get all confused and send you to a live person." So I did, and it worked.