  We extend our previous calculations of the hadronic light-by-light scattering
contribution to the muon anomalous magnetic moment in holographic QCD to models
with finite quark masses and a tower of massive pions. Analysing the role of
the latter in the Wess-Zumino-Witten action, we show that the
Melnikov-Vainshtein short-distance constraint is satisfied solely by the
summation of contributions from the infinite tower of axial vector meson
contributions. There is also an enhancement of the asymptotic behavior of
pseudoscalar contributions when their infinite tower of excitations is summed,
but this leads only to subleading contributions for the short-distance
constraints on light-by-light scattering. We also refine our numerical
evaluations, particularly in the pion and $a_1$ sector, which corroborates our
previous findings of contributions from axial vector mesons that are
significantly larger than those adopted for the effects of axials and
short-distance constraints in the recent White Paper on the Standard Model
prediction for $(g-2)_\mu$.
