DNA fragments can be sorted according to size by forcing them through an array of nanoposts. Whereas previous studies have explored solid nanoposts, this work examines nanoposts constructed out of viscous inclusions. Langevin dynamics simulations are used to study the dynamics of polymers driven through arrays of these viscous nanoposts for a range of post viscosities. The results are compared to the solid post case. Increasing post viscosity causes a decrease in the mobility of polymers traversing the array. In the limit of high post viscosity, the mobility becomes lower than in the solid post arrays, rather than converging to it. Analysis of the distributions of event times also shows that the viscous case is fundamentally different from the solid post case. The decrease in mobility in the viscous case arises from slowing down the polymer as it interacts with or even moves through the nanoposts, whereas the solid post case exhibits wrapping and unwrapping dynamics, yielding escape-like statistics. This work suggests that it may be possible to use viscous inclusions within nanofluidic and microfluidic devices to sort biomolecules with high resolution.