You can solve the problem in two easy steps: When your front foot is below your back foot take a normal stance with a “centered” ball position then move your lead foot down the hill and tilt your shoulders with the slope (see the photo below). Setting up this way delofts the club so use a higher-lofted wedge.
The two keys to achieving this goal are to a) make sure your clubhead makes clean contact with the ball and b) select a safe escape route to your target that’s ahead of where you would have been with a better swing.
Raymond Floyd who grabbed his lone U.S Open here in 1986 recently tipped me off to this Shinnecock secret. If you moved every hole so that each tee box originated at the clubhouse you’d discover how Shinnecock forces you to play toward all points on the compass.