NASA added a drag chute to the Space Shuttle (I believe during the design review following the Challenger accident). If you look at some of the landing video before the drag chute was added, there are some scary "directional excursions". If directional stability is your goal, I'm not sure that the Space Shuttle is a good starting point. Keep in mind that if your stabilizer is effective and the split rudder doesn't deploy symmetrically, you can expect a pretty good swerve.