Transition metal dichalcogenide superlattices provide an exciting new platform for exploring and understanding a variety of phases of matter. The moiré continuum Hamiltonian, of two-dimensional jellium in a modulating potential, provides a fundamental model for such systems. Accurate computations with this model are essential for interpreting experimental observations and making predictions for future explorations. In this work, we combine two complementary quantum Monte Carlo (QMC) methods, phaseless auxiliary field quantum Monte Carlo and fixed-phase diffusion Monte Carlo, to study the ground state of this Hamiltonian. We observe a metal-insulator transition between a paramagnet and a 120° Néel ordered state as the moiré potential depth and the interaction strength are varied. We find significant differences from existing results by Hartree-Fock and exact diagonalization studies. In addition, we benchmark density-functional theory, and suggest an optimal hybrid functional which best approximates our QMC results.