I think I probably confused myself by thinking about the Hamiltonian and low/high energies instead of just considering the values of L and S needed to get to the J-values associated with the energy levels.
When considering that J = L + S, J=0 would suggest antiparallel alignment for L and S to “cancel” each other.
With the same reasoning, J=2 needs a parallel alignment of S and L and the remaining J=1 corresponds to an orthogonal alignment.