Transport of rodlike particles in macromolecular networks is crucial in biology and technology. This study investigates the dynamics of thick rods (diameter comparable to network mesh size), a ubiquitous yet poorly understood case. Combining experiments, simulations, and theory, a non-monotonic dependence of translational diffusion on rod length is revealed, with unconventionally fast dynamics occurring when rod length is an integral multiple of the mesh size. This fast diffusion is attributed to sliding dynamics, which is shown to be anomalous yet Brownian. Theoretical analysis corroborates the sliding dynamics as an intermediate regime between hopping and Brownian dynamics, explained by a rod-length-dependent entropic free energy barrier. This work provides principles for designing efficient rodlike particle transport in macromolecular networks.