Coexistence of excitons and free charge carriers can complicate conventional spectroscopic studies of transport mechanisms in layered perovskite solar cells. Because of their large concentrations and absorbance cross sections, excitons tend to dominate spectroscopic signals and obscure observations of free charges in this class of systems. To investigate the effects of interstitial organic molecules on charge transport in photovoltaic devices, we apply a newly developed four-pulse transient grating method with photocurrent detection to layered perovskites possessing a range of quantum well thicknesses. In this method, a phase-stabilized "pump" pulse-pair photoexcites a carrier density grating in the active layer of a photovoltaic cell, whereas transport is time-resolved using the carrier density grating generated by a subsequent "probe" pulse-pair. Carrier diffusion mechanisms are revealed by measuring the recombination-induced nonlinear response of the device while varying the delay between pulse-pairs and phase difference between density gratings. Like drift velocity dispersion, our data suggest that encounters with inorganic-organic interfaces broaden the range of diffusivities in addition to skewing the distributions toward slower transit times. Rather than tunneling through the potential energy barriers associated with the organic material, the experimental measurements support a physical picture in which the photoexcited carriers traverse circuitous paths through the active layer while occupying the phases of the thickest quantum wells.