Recent studies in the feedback control of Rayleigh-Bénard convection indicate that one can sustain the no-motion state at a moderate supercritical Rayleigh number (Ra) using only proportional compensation. However, stabilization occurs at a much higher Rayleigh number using linear-quadratic-Gaussian (LQG) control synthesis. The restriction is that the convection model is linear. In this paper, we show that a comparable degree of stabilization is achievable for a fully nonlinear convection state. The process is demonstrated in two stages using a fully nonlinear, 3D Boussinseq model, compensated by a reduced-order LOQ controller and a gain-schedule table. In the first stage a fully-developed convective state is suppressed through the control action at a moderate supercritical Ra. After the residual convection decays to a sufficiently small amplitude, in the second stage, we increase the Ra by a large step and switch the compensator gains using the gain-schedule table. During this change the control action is in place. Our nonlinear simulation results suggest that the nonlinear system can be stabilized to the limit predicted by the linear analysis. The simulation shows that the large Ra jump induces a large transient temperature in the conductive component, which appears to have very small impact on the stabilization.