Unmanned aerial vehicles (UAVs) fill coverage holes as wireless relays during emergency situations. Fixed-wing UAVs offer longer flight duration and larger coverage in such situations than rotary-wing counterparts. Maximizing the effectiveness of fixed-wing UAV relay systems requires careful tuning of system and flight parameters. This process is challenging because factors including flight trajectory, timeshare, and user scheduling are not easily optimized. In this paper, we propose an optimization for UAV-based wireless relaying networks based on a setup which is applicable to arbitrary spatial user positions. In the setup, a fixed-wing UAV flies over a circular trajectory and relays data from ground users in a coverage hole to a distant base station (BS). Our optimization iteratively maximizes the average achievable spectral efficiency (SE) for the UAV trajectory, user scheduling, and relay timeshare. The simulation results show that our optimization is effective for varying user distributions and that it performs especially well on distributions with a high standard deviation.