We propose a System Level Synthesis (SLS) Model Predictive Control (MPC) approach to guidance and control (G&C) of the relative orbit for spacecraft rendezvous. SLS-MPC jointly optimizes a nominal trajectory and linear correction policy via convex optimization, which provides improved performance and feasibility with respect to practical Robust MPC (RMPC) methods, namely Linear Tube-Based MPC, which solely optimizes the nominal trajectory. Although this improvement comes at the cost of increased computational complexity, we show that a single initial SLS optimization can generate a nominal trajectory and correction policy that achieves performance comparable to standard RMPC, in a strategy which we call One-Shot SLS-MPC. Therefore, SLS can soften the dependence of MPC on real-time and recursive optimization, and more so given that the sole crucial optimization problem may be solved prior to the manoeuvre start while maintaining a time-flexible and safe hold point. Alternative deployment strategies are also discussed, which allow for trading-off between G&C performance and computational complexity. We also leverage a relative orbital element (ROE) state representation, in particular to formulate a novel simple and convex passive safety path constraint with limited conservativeness, and a dynamical prediction model that includes both