There are some interesting points coming out of this discussion. One of these is made by Dave Mac when he observes the effect of trying to right the boat with the mast downwind. Because the hull is pushed along by the wind, the sails will act against the interests of the helm and crew trying to right the boat (like a shovel).
I should therefore qualify my assertion on the direction that the boat should be righted. If the boat has turtled it makes sense (if you have the presence of mind) to start the righting process as though you are going to lift the mast to windward. As the mast breaks the water’s surface, pause, let the wind blow the mast round to a leeward position, then finish the righting manoeuvre.
Everyone else probably realised this years ago, but I never gave it much thought until now!