In response to newly found security vulnerabilities, or as part of a moving target defense, a fast and safe control software update scheme for networked control systems is highly desirable. We here develop such a scheme for intelligent electronic devices (IEDs) in power distribution systems, which is a solution to the so-called software update rollout problem. This problem seeks to minimize the makespan of the software rollout, while guaranteeing safety in voltage and current at all buses and lines despite possible worst-case update failure where malfunctioning IEDs may inject harmful amounts of power into the system. Based on the nonlinear DistFlow equations, we derive linear relations relating software update decisions to the worst-case voltages and currents, leading to a decision model both tractable and more accurate than previous models based on the popular linearized DistFlow equations. Under reasonable protection assumptions, the rollout problem can be formulated as a vector bin packing problem and instances can be built and solved using scalable computations. Using realistic benchmarks including one with 10,476 buses, we demonstrate that the proposed method can generate safe and effective rollout schedules in real-time.