Large offshore wind farms can trigger atmospheric gravity waves, with the associated hydrostatic blockage effect impacting their energy yield. Unfortunately, to date no tools exist that can model this wind-farm gravity-wave interaction and blockage at a computational cost that is not drastically higher than conventional engineering wake models. To address this, this paper applies insights from two-scale momentum (2SM) theory to an atmospheric perturbation model (APM), thereby significantly speeding up the latter. This leads to two different models, with one using pre-computed farm-level coefficients to compute the turbine forces and power output, while the other relies on repeated wake model evaluations. The core 2SM hypothesis and both developed models are validated using a prior LES dataset of a large wind farm. Both fast 2SM—APMs perform well, predicting blockage-corrected farm power at a computational cost that is only a factor 40 slower than a standalone wake model.