We investigate the problem of sparse target detection from widely distributed multistatic Frequency Modulated Continuous Wave (FMCW) radar systems (using chirp modulation). Unlike previous strategies (e.g., developed for FMCW or distributed multistatic radars), we propose a generic framework that scales well in terms of computational complexity for high-resolution space-velocity grid. Our approach assumes that (i) the target signal is sparse in a discrete space-velocity domain, hence allowing for non-static target detection, and (ii) the resulting multiple baseband radar signals share a common support. By simplifying the representation of the FMCW radar signals, we propose a versatile scheme balancing complexity and detection accuracy. In particular, we design a low-complexity, factorized alternative for the Matching Pursuit algorithm leveraging this simplified model, as well as an iterative methodology to compensate for the errors caused by the model simplifications. Extensive Monte-Carlo simulations of a K-band radar system show that our method achieves a fast estimation of moving target's parameters on dense grids, with controllable accuracy, and reaching state-of-the-art performances compared to previous sparsity-driven approaches.