Large-scale surveys will provide spectroscopy for ~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 ~30 abundances for eight metal-poor red giants in M15. From degraded quality Keck/HIRES spectra, we evaluate trends with resolution and signal-to-noise ratio (S/N) and find that (i) ~20 abundances are recovered consistently within <~0.1dex agreement and with <~0.05-0.15 dex systematic uncertainties from 10000<~R<~80000; (ii) for nine elements (C, Mg, Ca, Sc, Ti, Fe, Ni, Y, and Nd), this systematic precision and accuracy extends down to R~2500; and (iii) while most elements do not exhibit strong S/N-dependent systematics, there are nonnegligible biases for four elements (C, Mg, Ca, and Dy) below S/N~10/pixel. We compare statistical uncertainties from Markov Chain Monte Carlo sampling to the easier-to-compute Cramer-Rao bounds and find that they agree for ~85% 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 in the low-metallicity regime, and ongoing improvements to stellar models (e.g., 3D-NLTE physics) will only further extend its viability to more stars, more elements, and higher precision and accuracy.