As you say, the other two carriages change direction as you cross the edge of the triangle.
Your maximum extent is when one of the rods is horizontal i.e. an arc with a radius of your rod length and centred on the ball-joint of that tower. The maximum length of a rod is then the distance between the towers, less a bit for the size of the effector. If you were careful with your object design and position and had a large range in the angles of the ball-joints, I guess you could even exceed that? Of course, when you lengthen the rods, you sacrifice some height. The carriage with the horizontal rod has to move large distances for small changes in the effector position... this may limit your printing speed.