A new moiré material platform was recently proposed based on twisting two-dimensional atomic monolayers whose low-energy states lie at the three M-points of the Brillouin Zone. Continuum and ab initio modeling suggest that electrons in the conduction bands of these materials realize three-valley Hubbard models with valley-selective, quasi-one-dimensional hopping. Remarkably, the onsite Hubbard repulsion is almost U(6)-symmetric without fine-tuning. Here, we show that this class of systems naturally admits sign-free determinantal Quantum Monte Carlo simulations at a filling of three electrons per moiré unit cell. We use these to explore the phase diagram for interactions of various strengths and U(6)-breaking anisotropies. We show that for near-isotropic interactions as relevant to, e.g., AA-stacked twisted SnSe₂, the system exhibits an extended intermediate-coupling regime in which local-moment formation and itinerancy compete, and the crossover to a putative low-temperature ordered state can be understood in terms of fluctuating U(6) local moments. We argue that many of these features persist beyond the idealized sign-problem-free limit.