  We revisit cosmological constraints on the sum of the neutrino masses $\Sigma
m_\nu$ from a combination of full-shape BOSS galaxy clustering [$P(k)$] data
and measurements of the cross-correlation between Planck Cosmic Microwave
Background (CMB) lensing convergence and BOSS galaxy overdensity maps
[$C^{\kappa \text{g}}_{\ell}$], using a simple but theoretically motivated
model for the scale-dependent galaxy bias in auto- and cross-correlation
measurements. We improve upon earlier related work in several respects,
particularly through a more accurate treatment of the correlation and
covariance between $P(k)$ and $C^{\kappa \text{g}}_{\ell}$ measurements. When
combining these measurements with Planck CMB data, we find a 95% confidence
level upper limit of $\Sigma m_\nu<0.14\,{\rm eV}$, while slightly weaker
limits are obtained when including small-scale ACTPol CMB data, in agreement
with our expectations. We confirm earlier findings that (once combined with CMB
data) the full-shape information content is comparable to the geometrical
information content in the reconstructed BAO peaks given the precision of
current galaxy clustering data, discuss the physical significance of our
inferred bias and shot noise parameters, and perform a number of robustness
tests on our underlying model. While the inclusion of $C^{\kappa
\text{g}}_{\ell}$ measurements does not currently appear to lead to substantial
improvements in the resulting $\Sigma m_{\nu}$ constraints, we expect the
converse to be true for near-future galaxy clustering measurements, whose shape
information content will eventually supersede the geometrical one.
