The pilot in the experimental amateur-built, tailwheel-equipped airplane reported that during the landing roll, when the tailwheel touched down, the airplane veered to the right. He increased the engine power to increase the airflow around the rudder, but the airplane then veered to the left and exited the left side of the runway. With full throttle applied and full flaps, and unaware of his airspeed, he initiated a climb. However, the left main landing gear struck a taxiway sign, and the airplane became airborne. The pilot reduced the throttle to idle and the airplane touched down on the grass safety area and stopped. The airplane sustained substantial damage to the left main landing gear attachment points. The pilot reported that there were no mechanical malfunctions or failures with the airplane that would have precluded normal operation.