I don't know if this will help, as I have not traced my husband's family back beyond a few generations. My husband Marc Rademacher's father John Norman Rademacher was raised in East Aurora, NY. His father's name was also John Rademacher, one of 10 or 11 children including two named Francis Xavier. I believe there are Catherines and Anns in the past few generations. I was given to understand that in this branch of the Rademacher family, in at least ten consecutive generations, the eldest sons were named John. You might want to check out archives from the upstate New York area.
I can give you more specific information on this branch of the family if you would like. I just need a few days to pester my father in law.