Since you are not making an animation, you can use gravity to help you :)

Once you have the final pose you are after in the last frame. Go to frame 1 and rotate the horse and rider around 90 degree clockwise (maybe less) and do the same in the final frame. Since the cloth will always fall downwards you will get the effect of the rider riding fast forward. Then once its done calculating you add one frame in the end and rotate the horse and rider back to normal position, just make sure that the cloth is parented to the rider. I would be surprised if you wouldn't get some good results doing that. :) And if you need more speed, maybe move the horse and rider slightly upwards in the final frame.