White smoke MAY indicate a head gasket failing, allowing coolant into the combustion chamber. However, this can usually be diagnosed more accurately before pulling a cylinder head. This failure is also pretty rare. Cost to pull one or both heads would be $$$$... ton of labor, and a lot of "while you're in there" work to be done, causing the price to increase further. Is there another reputable mechanic in the area you could visit for a second opinion?
@gerryvz - anything obvious I'm forgetting here?