Computational models of language are having an increasing impact in understanding the neural bases of language processing in humans. A recent model of cortical dynamics based on reservoir computing was able to account for temporal aspects of human narrative processing as revealed by fMRI. In this context the current research introduces a form of structured reservoir computing, where network dynamics are further constrained by the connectivity architecture in order to begin to explain large scale hierarchical network properties of human cortical activity during narrative comprehension. Cortical processing takes place at different time scales depending on the position in a "hierarchy" from posterior sensory input areas to higher level associative frontal cortical areas. This phenomena is likely related to the cortical connectivity architecture. Recent studies have identified heterogeneity in this posterior-anterior hierarchy, with certain frontal associative areas displaying a faster narrative integration response than much more posterior areas. We hypothesize that these discontinuities can be due to white matter connectivity that would create shortcuts from fast sensory areas to distant frontal areas. To test this hypothesis, we analysed the white matter connectivity of these areas and discovered clear connectivity patterns in accord with our hypotheses. Based on these observations we performed simulations using reservoir networks with connectivity patterns structured with an exponential distance rule, yielding the sensory-associative hierarchy. We then introduce connectivity shortcuts corresponding to those observed in human anatomy, resulting in frontal areas with unusually fast narrative processing. Using structured reservoir computing we confirmed the hypothesis that topographic position in a cortical hierarchy can be dominated by long distance connections that can bring frontal areas closer to the sensory periphery.