So, here is my update three months later in case anyone else runs into this problem. In the end, they finally accepted the documents. All that’s left now is the interview portion.
All of my messages I sent to NVC were pointless. They just kept telling me to check the document website. I think I sent three messages to them complaining that my documents were correct and each time they just told me to check that website.
I was asking my wife about the documents she has given me to submit and it turned out one of them was the birth certificate, so I’m not sure why they rejected that. Anyways we decided to try using the English household registration and her birth certificate in Chinese. Apparently that was the right choice as they accepted those documents and now were moving on to the next stage in the process.