Accurate quantification of diffuse, area-source methane emissions remains a key challenge in closing the gap between bottom-up and top-down estimates of the global methane budget. Existing measurement approaches are limited by spatial coverage and ability to interrogate diffuse sources in the presence of a time-varying background concentration. Here, we present a framework combining kilometer-scale path-averaged laser beam concentration measurements with an analytical Bayesian inverse modeling approach to simultaneously retrieve spatially distributed area-source methane fluxes and a time-varying background concentration, without requiring direct background subtraction. We evaluate the system through an Observing System Simulation Experiment (OSSE) using real meteorological data, realistic instrument and transport model error, and a representative laser beam geometry observing three distinct but diffuse area sources. The inversion framework accurately retrieves weekly average emission rates across a wide range of flux magnitudes, with well-constrained estimates achievable for near-beam sources at median concentration enhancements as low as 1 ppb above background. We demonstrate the utility of running an ensemble of inversions to provide more robust emission estimates in the presence of uncertain prior flux distribution parameters. The system maintains accuracy within 10 % flux sources characterized in the prior even when a nearby emitting source is not represented in the prior estimate. This framework expands the conditions over which path-averaged laser concentration measurements can be used for area-source emission quantification and provides a pathway for optimizing future real-world deployments.