My husband's ancestor James R. Rambo was in Chickasaw Co, Indian Territory in 1900 living with his married son and daughter-in-law. As you gather the names of your family if you come across a possible connection, get back to me. I'd be happy to share what I know on the Rambos. I have them in SC, then down into GA, then AL, MS, TX, AR, OK, back to TX and finally out to CA.
There are two families in SC with sons named James (my husband has 4 direct generations of James Rambos beginning with his grandfather), one of the families in SC would be the connection on back to the immigrant ancestor Peter Rambo. The men in SC are brothers, so I know my husband's line goes directly back to Peter Rambo, just haven't proven which brother in SC is the direct link.