The response of slender structures exposed to wind flow exhibits various nonlinear behaviors, depending on the ratio between the natural and excitation frequencies. In the lock-in regime, the response becomes stationary; however, due to the nonlinearity of the model, its probability distribution is typically non-Gaussian. Outside the lock-in region, the response takes on a quasi-periodic character, with modulation patterns that depend on the distance from the lock-in boundary. Previous work by the authors demonstrated that averaged stationary response amplitudes can be characterized analytically under exact resonance. For slight detuning, however, numerical methods are required. The Galerkin approach using Hermite basis functions shows limitations, as it may produce nonphysical negative values in the probability density. This paper examines the non-stationary regime beyond lock-in, where the system exhibits quasi-periodic and modulated responses. The proposed methodology provides deeper insight into stochastic dynamics under both resonant and non-resonant conditions and is applicable to a broad range of problems, including traffic-induced vibrations, system identification, and aeroelastic instabilities.