We derive, in 2 + 1 dimensions, classical solutions for the metric and the motion of two or more spinning particles, in the conformal Coulomb gauge introduced previously. The solutions are exact in the N-body static case, and are perturbative in the particles' velocities in the dynamic two-body case. A natural boundary for the existence of our gauge choice is provided by some 'CTC horizons' encircling the particles, within which closed timelike curves occur.