Distribution system reconfiguration (DSR) uses switching actions, which are available to distribution system operators (DSOs) without regulatory changes, to optimize the grid topology. Although distribution systems often support meshed operation, they are typically operated radially to simplify fault isolation and improve reliability. The minimization of active power losses not only improves efficiency but also helps prevent voltage and current limit violations. However, the DSR problem is computationally difficult due to its combinatorial and non-convex nature. This paper proposes a cycle-basis-informed heuristic method for radial DSR, aiming to reduce active power losses and stabilize the voltage. The proposed heuristic method works directly with the non-convex AC load flow model, considering switching actions as the only degrees of freedom. A large neighborhood search framework is used, constructing restricted mixed-integer nonlinear programming (MINLP) subproblems of controllable complexity. Radiality is ensured via a graph-theoretic method based on the cycle basis of the system, enabling systematic exploration of feasible configurations. The proposed heuristic method is evaluated on benchmark systems with varying load profiles, demonstrating robust performance, effective loss reduction, improved voltage profiles, and practical computation time. These results confirm its applicability to real-world DSR in radial AC systems.