Transition metal dichalcogenides represent a versatile platform to study strong light-matter interactions based on excitons and electrons in ordered lattices. Twist-engineering of moiré structures further enables the manipulation of the polaritonic nonlinearities via engineering the exciton landscape on the nanoscale. In this work, we demonstrate in-situ control of the optical saturation-based nonlinearity of moiré exciton-polaritons by phase space restriction via charge doping. Strong exciton-photon coupling is established in a gate-controllable MoTe₂-MoSe₂ heterobilayer, embedded in a spectrally-tunable open cavity. A small gate voltage can effectively lower the necessary polariton density by one order of magnitude to achieve a similar nonlinear saturation effect as in the charge-neutral case. Our microscopic description successfully explains the observed phenomena in the framework of Pauli blocking for the moiré superlattices with charge preoccupation.