  Large-scale surveys will provide spectroscopy for $\sim$50 million resolved
stars in the Milky Way and Local Group. However, these data will have a high
degree of heterogeneity and most will be low-resolution ($R<10000$), posing
challenges to measuring consistent and reliable stellar labels. Here, we
introduce a framework for identifying and remedying these issues. By
simultaneously fitting the full spectrum and Gaia photometry with the Payne, we
measure $\sim$40 abundances for 8 red giants in M15. From degraded quality
Keck/HIRES spectra, we evaluate trends with resolution and S/N and find that
(i) $\sim$20 abundances are recovered consistently within $\lesssim$0.1 dex
agreement and with $\lesssim$0.05-0.15~dex systematic uncertainties from
$10000\lesssim R\lesssim80000$; (ii) for 9 elements (C, Mg, Ca, Sc, Ti, Fe, Ni,
Y, Nd), this systematic precision and accuracy extends down to $R\sim2500$; and
(iii) while most elements do not exhibit strong S/N-dependent systematics,
there are non-negligible biases for 4 elements (C, Mg, Ca, and Dy) below
$\text{S/N}\sim10$ pixel$^{-1}$. We compare statistical uncertainties from MCMC
sampling to the easier-to-compute Cram\'er-Rao bounds and find that they agree
for $\sim$75% of elements, indicating the latter to be a reliable and faster
way to estimate uncertainties. Our analysis illustrates the great promise of
low-resolution spectroscopy for stellar chemical abundance work, and ongoing
improvements to stellar models (e.g., 3D-NLTE physics) will only further extend
its viability to more elements and to higher precision and accuracy.
