Electronic close-coupling scattering calculations are reported on the relaxation process Ne+(2p(5) P-2(j1=1/2,m1))+He-->Ne+(2p(5) P-2(j2=3/2,m2))+He using a new interaction potential derived by combining spectroscopy and ab initio theory. Collision energies range from E/k(B)=300 K to less than 1 muK. As E is reduced, the total inelastic cross section sigma (j1-->j2)=sigma (1/2-->3/2) passes through a resonance-dominated regime and apparently approaches the Wigner limit below 10 muK, where the cross section is found to diverge in accord with the predicted E-1/2 dependence. A complex scattering length a = -53.0-0.04145i Angstrom is derived from the low-energy behavior. m-dependent alignment and orientation cross sections, sigma (j1\m1\-->j2\m2\) and sigma (j1m1-->j2m2), undergo rapid changes near resonances, and approach limiting behavior below 10 muK as well, while their ratios become asymptotically constant below 100 muK. Analysis of the scattering amplitude in the s-wave limit shows that the latter behavior is expected in general, with the ratios depending only on the geometry of angular momentum coupling. This geometrical effect disentangles s-wave dominance from the Wigner regime, and provides a new criterion for assessing the approach to the ultracold limit. Boltzmann averaging to simulate ultracold trapping conditions shows that a remnant of the resonance region and the characteristic limiting behavior remain observable.