The effects of non-adiabatic and Coriolis couplings on the bound states of the He(2 ^3S_1)+He(2 ^3P_j) system, where j=0,1,2, are investigated using the recently available ab initio short-range $^{1,3,5}Σ^+_{g,u}$ and $^{1,3,5}Π_{g,u}$ potentials computed by Deguilhem et al. (J. Phys. B: At. Mol. Opt. Phys. 42 (2009) 015102). Three sets of calculations have been undertaken: single-channel, multichannel without Coriolis couplings and full multichannel with Coriolis couplings. We find that non-adiabatic effects are negligible for $0^-_u,0^{±}_g,1_u,2_g,2_u,3_g$ Hund case (c) sets of levels in the j=2 asymptote but can be up to 15% for some of the $0^+_u$ and $1_g$ sets of levels where near degeneracies are present in the single-channel diagonalized potentials. Coriolis couplings are most significant for weakly bound levels, ranging from 1-5% for total angular momenta J=1,2 and up to 10% for J=3. Levels near the j=1 and j=0 asymptotes agree closely with previous multichannel calculations based upon long-range potentials constructed from retarded resonance dipole and dispersion interactions. Assignment of theoretical levels to experimental observations using criteria based upon the short-range character of each level and their coupling to metastable ground states produces well matched assignments for the majority of observations. After a 1% increase in the slope of the $^5Σ^+_{g,u}$ and $^5Π_{g,u}$ input potentials near the classical turning point is applied, improved matching of previous assignments is obtained and further assignments can be made, reproducing very closely the number of experimental observations. ; Comment: 22 pages; revisions in some values, additions to text, updated abstract, added 1 figure