For 3 more usable feet it would probably not be tough to do some layout, a few minutes of adz work and a touch up with a power planer to get rid of the twist. Just need to figure out how much will be left once straight, say 3x5 inches, and determine if that will carry the load at 11 feet. May only need a flat top and flat spots where it bears at the ends. Have to decide what your needs are, a lean-to may not require perfection.
