The Li-Haldane correspondence is often used to help identify wave functions of (2+1)-D chiral topological phases, by studying low-lying entanglement spectra (ES) on long cylinders of finite circumference. In the case of chiral topological phases that possess global Lie group symmetry, we describe how we can understand chiral ES in great detail through the splitting of degeneracies in the finite-size ES, at a given momentum, solely within the context of conformal field theory (CFT). We focus, in turn, on PEPS wave functions with global SU(2) and SU(3) symmetries. For SU(2), an intriguing observation is that in one topological sector of a PEPS, whose Li-Haldane counting and splittings are described by those of the non-Abelian SU(2)-level-two chiral spin-liquid, our analysis suggests in the large system size limit an ES with fractional (square-root) entanglement energy vs. wave vector dispersion law, indicating that it is not described by the standard CFT Hamiltonian. In the SU(3) case, we can contrast such chiral spectra with those of a non-chiral PEPS model with D(ℤ3) topological order, but with strong time-reversal and reflection symmetry breaking, that has an ES with branches of both right- and left-moving chiralities with vastly different velocities and an entanglement gap. The effect of this is that for finite circumference much smaller than the inverse entanglement gap scale, the low-lying ES of this system appears chiral in some topological sectors, precisely following the Li-Haldane state counting of a truly chiral SU(3)-level-one phase. Yet, a complete analysis of the ES reveals that this PEPS is in fact non-chiral. Having chiral and non-chiral SU(3) PEPS at our disposal, we can identify a distinct indicator of chirality in the ES: the splittings of conjugate representations in the ES. In the chiral ES, conjugate representations are exactly degenerate, because the operators (related to the cubic Casimir) that would be responsible for the splittings are forbidden by symmetry. In the non-chiral PEPS, these splittings are observed to be non-zero, and these operators lead to calculable splittings between conjugates.