Recent research has shown that when constrained to causality, the optimal feedback controller for an ocean wave energy converter (WEC) subjected to stochastic waves can be solved as a non-standard Linear Quadratic-Gaussian (LQG) optimal control problem. In this paper, we present a relaxation to the modeling assumptions that must be made to apply this theory. Specifically, we propose a technique that uses the principle of Gaussian Closure to accommodate nonlinear WEC dynamics in the synthesis of the optimal feedback law. The technique is approximate, in the sense that it arrives at a computationally efficient control synthesis technique through a Gaussian approximation of the stationary stochastic response of the system. This approach allows for a wide range of nonlinear dynamical models to be considered, and also accommodates many complex loss mechanisms in the power transmission system. The technique is demonstrated through simulation examples pertaining to a flap-type WEC with a hydraulic power train.