We continue the analysis which began in part 1 of this paper of the long-time behaviour of the fast rotations of a rigid body in an external analytic force field. Specifically, we consider the motions of a symmetric rigid body whose angular velocity is nearly parallel to the symmetry axis of the ellipsoid of inertia, which were excluded from the previous analysis because of the singularity of the action-angle coordinates. By suitably implementing the techniques of Nekhoroshev's theorem, so as to overcome this difficulty, we provide a description of these motions on timescales which grow with the angular velocity as ; such a description confirms the general properties of fast motions established in part 1.