We present new results from our ongoing study of flavor singlet pseudoscalar mesons in QCD. Our approach is based on (a) performing truncated eigenmode expansions for the hairpin diagram and (b) incorporating the ground state contribution for the connected meson propagator. First, we explain how the computations can be substantially improved by even-odd preconditioning. We extend previous results on early mass plateauing in the eta channel of two-flavor full QCD with degenerate sea and valence quarks to the partially quenched situation. We find that early mass plateau formation persists in the partially quenched situation.