The classical equilibrium wall model for large eddy simulations (LES) assumes that the wall shear stress has the same direction as the LES velocity at the wall model matching location. However, for flows exhibiting separation due to adverse pressure gradients this assumption is invalid when the matching location lies above the near-wall reversed flow region. Existing wall models cannot accommodate such situations of reverse stress with unresolved separation. We here extend the Moody diagram-based wall modeling method to incorporate velocity profiles with near-wall reversed flow. To avoid solving an ordinary differential equation to find the local wall stress during LES, the equation is solved off-line. The solution is fitted with highly accurate fitting functions, including in a parameter regime for which unresolved reverse flow occurs (strong adverse pressure gradient and low-to-moderate local Reynolds number). Analytic solutions are used to smoothly connect various asymptotic limits. The extended Moody diagram-based wall model is applied in LES of turbulent flow over periodic hills that exhibits local flow separation. While the wall model effect on mean velocity profiles is less easily elucidated due to additional dependencies on subgrid-scale model details and how the stress boundary condition is imposed, LES with the proposed extended Moody wall model yields improved predictions of the wall stress in the specific region where a separation bubble occurs below the matching height.