The Magnetospheric Multiscale (MMS) mission has given us unprecedented access to high cadence particle and field data of magnetic reconnection at Earth's magnetopause. MMS first passed very near an X-line on 16 October 2015, the Burch event, and has since observed multiple X-line crossings. Subsequent 3D particle-in-cell (PIC) modeling efforts of and comparison with the Burch event have revealed a host of novel physical insights concerning magnetic reconnection, turbulence induced particle mixing, and secondary instabilities. In this study, we employ the Gkeyll simulation framework to study the Burch event with different classes of extended, multi-fluid magnetohydrodynamics (MHD), including models that incorporate important kinetic effects, such as the electron pressure tensor, with physics-based closure relations designed to capture linear Landau damping. Such fluid modeling approaches are able to capture different levels of kinetic physics in global simulations and are generally less costly than fully kinetic PIC. We focus on the additional physics one can capture with increasing levels of fluid closure refinement via comparison with MMS data and existing PIC simulations. In particular, we find that the ten-moment model well captures the agyrotropic structure of the pressure tensor in the vicinity of the X-line and the magnitude of anisotropic electron heating observed in MMS and PIC simulations. However, the ten-moment model has difficulty resolving the lower hybrid drift instability, which has been observed to plays a fundamental role in heating and mixing electrons in the current layer.