Protonated hydrogen dimer, H₅⁺, is the intermediate in the astrochemically important proton transfer reaction between H₃⁺ and H2. To understand the mechanism for this process, we focus on how large amplitude motions in H₅⁺ result in scrambling of the five hydrogen atoms in the collision complex. To this end, the one-dimensional zero-point corrected potential surfaces were mapped out as functions of reaction coordinates for the H₃⁺ + H2 collision using minimized energy path diffusion Monte Carlo [C. E. Hinkle and A. B. McCoy, J. Phys. Chem. Lett. 1, 562 (2010)]. In this study, the previously developed approach was extended to allow for the investigation of selected excited states that are expected to be involved in the proton scrambling dynamics. Specifically, excited states in the shared proton motion between the two H2 groups, and in the outer H2 bending motions were investigated. Of particular interest is the minimum distance between H₃⁺ and H2 at which all five hydrogen atoms become free to exchange. In addition, this diffusion Monte Carlo-based approach was used to determine the zero-point energy E0, the dissociation energy D0, and excitation energies associated with the vibrational motions that were investigated. The evolution of the wave functions was also studied, with a focus on how the intramolecular vibrations in H₅⁺ evolve into motions of H₃⁺ or H2. In the case of the proton scrambling, we find that the relevant transition states become fully accessible at separations between H₃⁺ and H2 of approximately 2.15 Å, a distance that is accessed by the excited states of H₅⁺ with two or more quanta in the shared proton stretch. The implications of this finding on the vibrational spectroscopy of H₅⁺ are also discussed.