We study a one-dimensional exclusion process with a fixed jump length $I\ge 1$ in which a particle may advance or retreat $I$ sites provided all intermediate sites are vacant, with hopping rates of Arrhenius type depending on the local headway. We identify the class of rates admitting an explicit Ising–Gibbs invariant measure, with stationarity governed by pairwise balance rather than detailed balance. In the thermodynamic limit, we derive a closed-form stationary current. We also derive a closed mean-field expression for the stationary current using a propagation-of-chaos approximation. The exact and mean-field currents coincide in the non-interacting case, while non-trivial interactions lead to different stationary currents. For a preferred-spacing interaction, the exact stationary headway law can become bimodal, whereas the corresponding mean-field approximation gives a geometric headway distribution. The exact current is confirmed by kinetic Monte Carlo simulations and exact finite-size computations.