I think you are at the end of the line, Bill. Church records more or less started at this time, so finding earlier records is unlikely. The record does state "termo" de Ponte de Lima, not Carmo. This simply means it is within the limits of Ponte de Lima jurisdiction. Like Lomba de Maia is in the termo of Maia. In fact, Ribeira Grande has some of the earliest and best records I have seen anywhere. It doesn't get any better. Also, this is about the time when people started to use two or more names, so that makes it difficult to trace people with common names. If you connect to nobles and wealthy people, it may be possible to get back further. Most of that research is already done by professional genealogists and historians in various publications. And these are likely in Rodrigo Rodrigues works, as he traced many of the founding settlers back to the founding of the first settlements. Maybe Margaret can add something.
JR