My situation is almost exactly like this person’s Eligibility for NWOHR passport+TARC if no active household registration at time of birth. The only added complication is that my American father has all my mother’s documents and I am estranged from him. He would not send them if I asked. I guess I would have to wait until he dies so I can go through his stuff. I already have my ROC passport and have access to my mother’s HHR in Taiwan when she used to live there when she was a young adult before emigrating. The american marriage was never registered in Taiwan. Not sure if that needs to happen. Perhaps some other documents that the taiwan government has. That is about it. Her whole family still lives in Taiwan and can help me get what’s available there.
You (or your mother) should be able to request duplicate copies of any document that your estranged father has.
I lost my original birth certificate a long time ago, so I requested a duplicate copy from my State of birth.