Just throwing my two cents in from the about-to-be-defunct IMDb board, and two somewhat "established" outcomes in that forum:
A) John and Anna Bates name their son Norman, move to Southern California and open a motel. 'Nuff said.
B) Thomas Barrow moves to Texas to join his American cousins Clyde and Buck, Buck's wife Blanche and Clyde's mistress Bonnie in a multi-state armed bank robbery spree, using his skills as a veteran British Army medic to help patch up the gang after their multiple shootouts. After Buck is killed and Blanche is wounded and captured, he stashes all of the gang's loot. Then he phones in an anonymous tip to the Texas Rangers setting up Clyde and his mistress for an ambush. Then he exchanges the loot for Pounds Sterling, returns to Downton and buys out the estate from the Crawleys who have been wiped out by the Great Depression.
