  We perform a thorough examination of the neutrino mass ($M_\nu$) constraints
achievable by combining future spectroscopic galaxy surveys with cosmic
microwave background (CMB) experiments, focusing on the contribution of CMB
lensing and galaxy-CMB lensing. CMB lensing can help by breaking the
$M_\nu$-curvature degeneracy when combined with baryon acoustic oscillation
(BAO)-only measurements, but we demonstrate this combination wastes a great
deal of constraining power, as the broadband shape of the power spectrum
contributes significantly to constraints. We also expand on previous work to
demonstrate how cosmology-independent constraints on $M_\nu$ can be extracted
by combining measurements of the scale-dependence in the power spectrum caused
by neutrino free-streaming with the full power of future CMB surveys. These
free-streaming constraints are independent of the optical depth to the CMB
($\tau$) and competitive with constraints from BAOs for extended cosmologies,
even when both are combined with CMB lensing and galaxy-CMB lensing.
