We combine the linearized Boltzmann Transport Equation (LBTE) and quantum transport by means of the Non-equilibrium Green's Functions (NEGF) to simulate monolayer MoS2 and WS2 ultra-scaled transistors with carrier mobilities extracted from experiments. Electron-phonon, charged impurity, and surface optical phonon scattering are taken into account with all necessary parameters derived from ab initio calculations or measurements, except for the impurity concentration. The LBTE method is used to scale the scattering self-energies of NEGF, which only include local interactions. This ensures an accurate reproduction of the measured mobilities by NEGF. We then perform device simulations and demonstrate that the considered transistors operate far from their performance limit (from 50% for MoS2 to 60% for WS2). Higher quality materials and substrate engineering will be needed to improve the situation.