We investigate photon-current routing in a two-dimensional Rabi-Hofstadter lattice with nearest-neighbor and diagonal photon hopping. Complex-valued infinite projected entangled-pair-state calculations, supported by a semiclassical current-network analysis, show that the square flux establishes a chiral superradiant background, whereas diagonal hopping redistributes the current among square, triangular, and diagonal paths. For the parameters considered here, reversing the sign of the diagonal hopping enhances the triangular-loop response, while a triangular-flux imbalance selects one of the two diagonal channels. Their combined action produces square-dominant, triangular-enhanced, diagonal-selected, and mixed current textures. These textures are operational routing regimes within the superradiant phase rather than distinct thermodynamic phases.