Nanoparticles can greatly enhance the mechanical response of elastomeric polymers essential to a wide range of applications, yet their precise molecular mechanisms of high-strain reinforcement remain largely unresolved. Here we show, based on molecular dynamics simulations, that high-strain reinforcement emerges from an interplay between granular nanoparticulate compressive behavior in the normal direction and polymer incompressibility. This feedback loop, which is initiated by a mismatch in the Poisson ratios of nanofiller and polymer, invokes a contribution from the polymer's bulk modulus to the elongational stress, while the tendency of the polymer to contract in the normal direction maintains a near-jammed filler state. This effect persists even once the direct filler elongational contribution becomes dissipative after the 'Payne effect' yield. These results indicate that direct particle-particle contact effects, even in the absence of potential augmenting mechanisms such as glassy polymer bridges, can drive the mechanical reinforcement effects typical of experimental systems.