The low-energy dynamics of antiferromagnetic spin waves map onto a massive Klein-Gordon scalar field, providing a solid-state platform for analogue-horizon physics. We show that an inhomogeneous spin current generates an effective magnon flow capable of forming black- and white-hole horizons. Horizon-pair cavities exhibit resonant transport and superradiant-like amplification mediated by magnon-antimagnon mixing. Our central result is that a periodic arrangement of submagnonic and supermagnonic regions forms a non-reciprocal magnonic crystal in which entering the supermagnonic regime makes negative-norm propagating channels available and enables the bulk gap to close and reopen. This drives a topological transition characterized by a change in the Zak phase and the emergence of a hybrid magnon-antimagnon edge state. These results establish a direct connection between analogue-horizon physics and topological magnonics, providing an electrically tunable route for controlling magnonic band topology.