The local equivalence ratio distribution in a flame affects its shape and response under velocity perturbations. The forced heat release response of stratified lean-premixed flames to acoustic velocity fluctuations is investigated via chemiluminescence measurements and spatial Fourier transfer analysis. A laboratory scale burner and its boundary conditions were designed to generate high-amplitude acoustic velocity fluctuations in flames. These flames are subject to inlet radial equivalence ratio distributions created via a split annular fuel delivery system outfitted with a swirling stabilizer. Simultaneous measurements on the oscillations of inlet velocity and heat release rate were carried out via a two-microphone technique and OH* chemiluminescence. The measurements show that, for a given mean total power and equivalence ratio ($\phi g=0.60$), the flame responses vary significantly on the equivalence ratio split, forcing frequency, and velocity fluctuation amplitude, with significant nonlinearities with respect to forcing amplitude and stratification ratio (SR). The spatial Fourier transfer analysis shows how the dependence is affected by the underlying changes in the rate of heat release, including the direction and speed of the perturbation within the flame.