Most certainly Edgar Cayce was, and still is, very proud of his Grandson, Charles Thomas Cayce, who led the ARE for many years which revolved around the Edgar Cayce Readings which also revealed many reincarnations during life readings for individuals.
Charles Thomas was also given a reading which revealed that he was once Luke..The Readings also revealed that Edgar Cayce was the uncle of Luke, named Lucius who actually wrote the Gospel of Luke. Here is a link for more information on Charles Thomas....
http://www.edgarcayce.org/are/mediaGuidelines.aspx?id=13173