lots of those big slow flyers are like hot air balloons, they are great flyers but just pray the wind don't kick up or its gone.!! Wish I had a plane that flew like that, but then again how often do you get dead calm wind conditions...?
Aerofoil tails are actually quite common. Check out any of the Guillows balsa plane kits designed for long duration flight, such as the Javelin, or any highly-detailed scale aircraft. We just usually use flat profile tails because they're easy and we're lazy.