Coupling of space-separated resonators is interesting for quantum and communication technologies. In this work, we show that antiferromagnetic resonance in separated parallel-plane slabs of hematite (alpha-Fe2O3) couple cooperatively to terahertz electromagnetic cavity modes formed by the slabs themselves. We demonstrate control of these hybridized magnon-polariton modes either by tuning the distance between the slabs in the range of up to a few millimters or by scanning their temperatures in a range above room temperature. Analysis of measured spectra with three distinct theoretical models shows that the best approximations can be obtained with a model based on classical electromagnetism. Cavity-mediated coupling allows the engineering of resonators at millimeter-range frequencies (millielectronvolts).