In this letter, we propose an energy-efficient design for an unmanned aerial vehicle (UAV)-mounted reconfigurable intelligent surface (RIS) communication system with nonlinear energy harvesting (EH) and UAV jitter. A joint optimization problem is formulated to maximize the EH efficiency of the UAV-mounted RIS by controlling the user powers, RIS phase shifts, and time-switching factor, subject to quality of service and practical EH constraints. The problem is nonconvex and time-coupled due to UAV angular jitter and nonlinear EH dynamics, making it intractable for conventional optimization methods. To address this, we reformulate the problem as a deep reinforcement learning (DRL) environment and develop a smoothed softmax dual deep deterministic policy gradient algorithm. The proposed method incorporates action clipping, entropy regularization, and softmax-weighted Q-value estimation to improve learning stability and exploration. Simulation results show that the proposed algorithm converges reliably under various UAV jitter levels and achieves an average EH efficiency of 45.07\%, approaching the 53.09\% upper bound of exhaustive search, and outperforming other DRL baselines.