We revisit cosmological constraints on the sum of the neutrino masses Σm_ν 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_ℓ^κg], 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_ℓ^κg measurements. When combining these measurements with Planck CMB data, we find a 95% confidence level upper limit of Σm_ν<0.14eV, 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_ℓ^κg measurements does not currently appear to lead to substantial improvements in the resulting Σm_ν constraints, we expect the converse to be true for near-future galaxy clustering measurements, whose shape information content will eventually supersede the geometrical one.