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Neutron star glitches are commonly believed to occur, when angular momentum is transferred suddenly from the star's interior to the crust by the collective unpinning and repinning of large numbers of superfluid vortices. In general, the pinning potential associated with nuclei in the crustal lattice varies as a function of radius. We explore vortex dynamics under these conditions by solving the three-dimensional Gross-Pitaevskii equation in a rotating, harmonic trap with an axisymmetric `moat' of deeper pinning sites on an otherwise uniform, corotating pinning grid. The moat is designed to resemble crudely a radially dependent pinning profile in a neutron star crust, although the values of the pinning potential are not astrophysically realistic due to computational constraints. It is shown that vortices accumulate in the moat, inducing large differential rotation which can trigger mass unpinning events. It is also shown that the system self-adjusts, such that the net vortex flux out of the system is the same with and without a moat, as the trap spins down, but glitches are less frequent and larger when the moat is present. The results, generated for an idealized system, represent a first step towards including stratified pinning in quantum mechanical models of neutron star glitches.