Found this link with a listing of House of David players and "hired" players over the years. E.E. Ambrose looks to be Elmer Ambrose, a hired player. I can't find anything else about him. I can't tell you if the Alexander auto is authentic, but I can tell you that both he and Babe Didrikson both played in the 30's for House of David, so at least the story matches up. Good luck and hope you find it authentic.
http://houseofdavidbaseball.com/players/index.asp