We continue the analysis of models of spontaneous wavefunction collapse with stochastic dynamics driven by non-white Gaussian noise. We specialize to a model in which a classical 'noise' field, with specified autocorrelator, is coupled to a local nonrelativistic particle density. We derive general results in this model for the rates of density matrix diagonalization and of state vector reduction, and show that (in the absence of decoherence) both processes are governed by essentially the same rate parameters. As an alternative route to our reduction results, we also derive the Fokker-Planck equations that correspond to the initial stochastic Schrödinger equation. For specific models of the noise autocorrelator, including ones motivated by the structure of thermal Green's functions, we discuss the qualitative and quantitative dependence on model parameters, with particular emphasis on possible cosmological sources of the noise field.