That is a very interesting way of thinking about the landing. If you are going to use DOF, you should also mention the grid fins (4 DOF (1)), and how control ov

That is a very interesting way of thinking about the landing. If you are going to use DOF, you should also mention the grid fins (4 DOF (1)), and how control over parameters can be "time-shifted". Early in the descent the rotation of the craft doesn't matter so much as its trajectory, and so the grid fins can control pitch to aim for the landing site (2 DOF). Once the trajectory for landing is mostly established, the grid fins can be used to eliminate the vehicle rotation (3 DOF). At the time of landing, the grid fins are no longer useful, but they have set one degree of freedom that none of the other controls will change (rotation about the central axis of the rocket), so essentially they have "6 DOF in" at the time of landing. (1) In addition to control over rotation, the fins can be turned so that they cancel each other out overall, and thus slow down the vehicle without changing its rotation. I don't know whether the fins are actually used this way given the stresses involved.