The effect of corrugated grain boundaries on the frictional properties of extended graphitic contacts incorporating a polycrystalline surface are investigated. The friction is found to be dominated by shear induced buckling and unbuckling of corrugated grain boundary dislocations, leading to a nonmonotonic behavior of friction with normal load and temperature. The underlying mechanism involves two competing effects, where an increase of dislocation buckling probability is accompanied by a decrease of the dissipated energy per buckling event. These effects are well captured by a phenomenological two-state model, that allows for characterizing the tribological properties of any large-scale polycrystalline layered interface, while circumventing the need for demanding atomistic simulations. The resulting negative differential friction coefficients obtained in the high-load regime can reduce the expected linear scaling of grain-boundary friction with surface area and restore structural superlubricity at increasing length-scales.