Differential intensity measurements of interplanetary H, He, and O ions made with the Low-Energy Charged Particle (LECP) instruments aboard the Voyager 1 (V1) and Voyager 2 (V2) deep space probes and the Low-Energy Ion Composition Analyzer (LICA) aboard the near-Earth Solar Anomalous Magnetospheric Particle Explorer (SAMPEX) satellite provide a comprehensive perspective on the transport of anomalous cosmic ray (ACR) ions during the 1991--1999 recovery phase of solar cycle 22 in both the outer and inner heliosphere. We report fifteen unique, independent ACR intensity time series, ranging over kinetic energies from 0.6 to 40 MeV/nucleon, and parameterize these observations (supplemented by one time-intensity profile from the literature) with a four-parameter fitting function to quantify the ACR behavior as solar minimum conditions developed and the V1 and V2 probes ranged from 36 to 76 AU from the Sun. We discuss a possible physical explanation for the striking differences between the outer heliospheric ACR recovery profiles at various energies. The intensities of nearly all species and energies recovered similarly from 1991 to mid-1994, increasing about an order of magnitude, but differed in a rigidity-dependent manner during the subsequent 5 years with the low-rigidity particle intensities growing exponentially, increasing up to an order of magnitude, while the high-rigidity particle intensities remained nearly constant. We find that these observations support the interpretation that before 1994 the recovery profiles of all the ACRs were governed by a temporal mechanism probably driven by the timescale of the variation of the transport properties of the interplanetary medium itself, rather than the relaxation timescale for diffusive equilibrium to develop. After 1994 the motion of the Voyager probes through regions with stable, positive radial intensity gradients explains the diverse recovery profiles of the various ACR species.