  The astrophysical engines that power ultra-high-energy cosmic rays (UHECRs)
remain to date unknown. Since the propagation horizon of UHECRs is limited to
the local, anisotropic Universe, the distribution of UHECR arrival directions
should be anisotropic. In this paper we expand the analysis of the potential
for the angular, harmonic cross-correlation between UHECRs and galaxies to
detect such anisotropies. We do so by studying simulations performed assuming
proton, oxygen and silicon injection models, each simulation containing a
number of events comparable to a conservative estimate of currently available
datasets, as well as by extending the analytic treatment of the magnetic
deflections. Quantitatively, we find that, while the correlations for each
given multipole are generally weak, (1) the total harmonic power summed over
multipoles is detectable with signal-to-noise ratios well above~5 for both the
auto-correlation and the cross-correlation (once optimal weights are applied)
in most cases studied here, with peaks of signal-to-noise ratio around
between~8 and~10 at the highest energies; (2) if we combine the UHECR
auto-correlation and the cross-correlation we are able to reach detection
levels of (3\sigma) and above for individual multipoles at the largest scales,
especially for heavy composition. In particular, we predict that the
combined-analysis quadrupole could be detected already with existing data.
