Flapping-fin unmanned underwater vehicle (UUV) propulsion systems provide high maneuverability for naval tasks such as surveillance and terrain exploration. Recent work has explored the use of time-series neural network surrogate models to predict thrust from vehicle design and fin kinematics. We develop a search-based inverse model that leverages a kinematics-to-thrust neural network model for control system design. Our inverse model finds a set of fin kinematics with the multi-objective goal of reaching a target thrust and creating a smooth kinematic transition between flapping cycles. We demonstrate how a control system integrating this inverse model can make online, cycle-to-cycle adjustments to prioritize different system objectives.