Our approach significantly expands the problem scale compared to prior research in related studies by efficiently solving large-scale problems often encountered in practice. Further, the high modularity of our algorithm allows users to incorporate their own methods and models, such as wind and emission distribution estimators (in cases with limited or no existing wind data) or different atmospheric transport models. As such, the algorithm holds substantial practical value, particularly as the use of Continuous Monitoring Systems (CMS) becomes increasingly prevalent and critical in the quest to rapidly reduce methane emissions.