Kerr naked singularities (superspinars) have to be efficiently converted to a black hole due to accretion from Keplerian discs. In the final stages of the conversion process the near-extreme Kerr naked singularities (superspinars) provide a variety of extraordinary physical phenomena. Such superspinning Kerr geometries can serve as an efficient accelerator for extremely high-energy collisions enabling direct and clear demonstration of the outcomes of the collision processes. We shall discuss the efficiency and visibility of the ultra-high-energy collisions in the deepest parts of the gravitational well of superspinning near-extreme Kerr geometries for the whole variety of particles freely falling from infinity. We demonstrate that the ultra-high-energy processes can be obtained with no fine tuning of the motion constants and the products of the collision can escape to infinity with both directional and energetical efficiency significantly higher than in the case of the near-extreme black holes. The strongest efficiency of the collision process is reached for particles falling along trajectories with maximally acceptable negative angular momentum.