I think I finally found the answer to Alexander. My first clue came when I went to the Archives yesterday and in the NS census of 1773 Alexander had told the census taker that he was American and not Scottish. After further investigation it seems he was born in Sandwich Massachusetts on Jan 1st 1773. His father's name was Alexander and his mother's name was Beulah Ann Schoville. It is still reasonable that his family came to Nova Scotia on a ship with went down and that Alexander was the only survivor since in the Yarmouth census of 1773 he is the only Bain on the list. I'm looking further...interesting!