The end-Cretaceous mass extinction was marked by both the Chicxulub impact and the ongoing emplacement of the Deccan Traps flood basalt province. To understand the mechanism of extinction, we must disentangle the timing, duration, and intensity of volcanic and meteoritic environmental forcings. In this study, we used a parallel Markov chain Monte Carlo approach to invert for carbon dioxide (CO2) and sulfur dioxide (SO2) emissions, export productivity, and remineralization from 67 to 65 million years ago using the LOSCAR (Long-term Ocean-atmosphere-Sediment CArbon cycle Reservoir) model. Our results closely match observed and proxy data and suggest decoupled CO2 and SO2 emissions, a two-step decline in export productivity with a protracted recovery, and no clear volatile impulse at the boundary. More broadly, our methods provide a potential path forward for efficient parallel inversion of complex Earth system models.