We present a comprehensive classical model of large-scale angular momentum transfer in alkali Rydberg atoms by collisions with ions near or below the matching velocity, at which the speed of the colliding ion equals the classical, average speed of the Rydberg electron. We model the atomic quantum defect by perturbative methods, and obtain excellent agreement with experiments measuring the total collision cross section and the collisional population of individual high-l states. At the matching velocity, or right below it, the final distribution of angular momenta is peaked along the direction of the ionic beam, which indicates that the population of the m(l) sublevels is not uniform. We apply our model to intrashell {n,l}-->{n,l＇} transitions induced by ion-Rydberg collisions under zero-electron-kinetic-energy photoelectron spectroscopy (ZEKE-PES) conditions, and demonstrate that the excitation of ultra-long-lived Rydberg states via ion-Rydberg collisions is a two-step mechanism : First, a collision quenches the quantum defect, but fails to bring about a complete statistical mixing of levels. Subsequent collisions excite preferentially the ultra-long-living, high-l states (ZEKE states) which are mostly responsible for the ZEKE signal.