Classical approaches to experimental design assume that intervening on one unit does not affect other units. There are many important settings, however, where this non-interference assumption does not hold, e.g., when running experiments on supply-side incentives on a ride-sharing platform or subsidies in an energy marketplace. In this paper, we introduce a new approach to experimental design in large-scale stochastic systems with considerable cross-unit interference, under an assumption that the interference is structured enough that it can be captured using mean-field asymptotics. Our approach enables us to accurately estimate the effect of small changes to system parameters by combining unobstrusive randomization with light-weight modeling, all while remaining in equilibrium. We can then use these estimates to optimize the system by gradient descent. Concretely, we focus on the problem of a platform that seeks to optimize supply-side payments p in a centralized marketplace where different suppliers interact via their effects on the overall supply-demand equilibrium, and show that our approach enables the platform to optimize p based on perturbations whose magnitude can get vanishingly small in large systems.[-]