You're welcome. The name Basil doesn't sound Irish to me. I believe it was originally from the Mediterranean area and is more common in England than in Ireland.
There is still a possibility that you're connected to my line that starts with Peter PORTER 1,2,3. The first migrated to Jamestown, VA, where he is found on the 1624 census "at the Eastern Shore" and in 1625 at Elizabeth City, VA, having come on the Tiger in 1621. He later moved to Anne Arundel Co., MD.
Wm. Arthur PORTER published a book on Peter's family, but for the first three generations, only those named Peter are included. Of the names in your family, I only see Charles in my early Porter families.
NEVER GIVE UP!