The pilot reported that he intended to land the tailwheel-equipped airplane on a sloped asphalt runway that he had not landed at before the accident flight. The first landing attempt terminated with a go-around because he was not comfortable with the approach. The second approach was high and a little too fast, which caused the airplane to float down the runway. When the airplane touched down, it bounced; after a second bounce, the pilot applied increasingly aggressive braking for fear of overrunning the runway. The airplane veered off the hard surface runway, encountered soft mud, and subsequently nosed over, resulting in substantial damage to the vertical stabilizer, rudder, and elevator. The pilot reported no preimpact mechanical malfunctions or failures with the airplane that would have precluded normal operation.