In general, detailed mechanistic models for fuel cell stacks that seek to capture the local transport phenomena are computationally expensive. In this context, we propose a hybrid modeling strategy, in which the steady-state conservation equations are solved iteratively in two separate groups: The first comprises asymptotically-reduced governing equations for momentum, mass, and species, which are solved as a transient-like propagation problem; the second comprises the full set of equations for energy and charge, which are solved as an elliptic stationary problem. Physically, the segregation is justified by the nature of the dependent variables; in essence, the first group covers local variables on the cell level and the second involves global variables on the stack level. We demonstrate the methodology for a steady-state detailed mechanistic model of a proton exchange membrane fuel cell stack comprising 2 to 350 cells subjected to non-uniform operating conditions across the cells; e.g., a stack comprising 350 cells takes less than an hour to solve. The proposed methodology is generic and can also be employed for other systems where transport phenomena occur on different length scales and involve some form of slenderness.