It has recently been shown that X-ray parametric down-conversion (XPDC) provides access to high-energy polaritons, resulting from the hybridization of down-converted photons with electronic excitations in a nonlinear medium. Here, we present a spectrally resolved study of this effect around the K-shell absorption edge in diamond. Our results exhibit pronounced signatures of polaritonic hybridization, which we visualize by introducing a polariton spectral map and analyze by help of theoretical modelling. We find that the hybridization at this absorption edge results in substantially higher coupling strength than previously reported for a non-resonant case and reaches well into the strong-coupling regime. In addition, we demonstrate how our measurements of polaritonic XPDC allow us to extract the refractive index for bulk diamond at high spectral resolution around the carbon K-edge.