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The electron runaway phenomenon in plasmas depends sensitively on the momentum-space dynamics. However, efficient simulation of the global evolution of systems involving runaway electrons typically requires a reduced fluid description. This is needed for example in the design of essential runaway mitigation methods for tokamaks. In this paper, we present a method to include the effect of momentum-dependent spatial transport in the runaway avalanche growth rate. We quantify the reduction of the growth rate in the presence of electron diffusion in stochastic magnetic fields and show that the spatial transport can raise the effective critical electric field. Using a perturbative approach we derive a set of equations that allows treatment of the effect of spatial transport on runaway dynamics in the presence of radial variation in plasma parameters. This is then used to demonstrate the effect of spatial transport in current quench simulations for ITER-like plasmas with massive material injection. We find that in scenarios with sufficiently slow current quench, due to moderate impurity and deuterium injection, the presence of magnetic perturbations reduces the final runaway current considerably. Perturbations localized at the edge are not effective in suppressing the runaways, unless the runaway generation is off-axis, in which case they may lead to formation of strong current sheets at the interface of the confined and perturbed regions.