We present a broad, multi-wavelength study of RXC J2014.8-2430, the most extreme cool-core cluster in the Representative XMM-Newton Cluster Structure Survey (REXCESS), using Chandra X-ray, Southern Astrophysical Research (SOAR) Telescope spectroscopic and narrow-band imaging, Atacama Large Millimeter/submillimeter Array (ALMA), Very Large Array, and Giant Metrewave Radio Telescope observations. While feedback from an active galactic nucleus (AGN) is thought to be the dominant mechanism by which a cooling flow is suppressed, the Chandra imaging observations surprisingly do not reveal the bi-lateral X-ray cavities one might expect to see in the intracluster medium (ICM) of an extreme cool core hosting a powerful radio source, though cavities commonly appear in many similar sources. We discuss the limits on the properties of putative radio bubbles associated with any undetected X-ray cavities. We place upper limits on any significant X-ray AGN in the brightest cluster galaxy (BCG) and show that the X-ray peak is offset from the central radio source, which exhibits a steep low-frequency radio spectrum indicative of electron ageing. The imaging and spectroscopy provided by SOAR reveal an extended, luminous optical emission-line source. From our narrow-band Hα imaging of the BCG, the central Hα peak is coincident with the radio observations, yet offset from the X-ray peak, consistent with sloshing found previously in this cluster. ALMA observations of the CO(1-0) emission reveal a large reservoir of molecular gas that traces the extended Hα emission in the direction of the cool core. We conclude either that the radio source and its cavities in the X-ray gas are nearly aligned along the line of sight, or that ram pressure induced by sloshing has significantly displaced the cool molecular gas feeding it, perhaps preempting the AGN feedback cycle. We argue that the sloshing near the core is likely subsonic, as expected, given the co-location of the Hα, CO(1-0), radio continuum, and stellar emission peaks and their proximity to the X-ray peak. Further, the X-ray emission from the core is strongly concentrated, as is the distribution of metals, indicating the cool core remains largely intact. Deeper Chandra observations will be crucial for definitively establishing the presence or lack of X-ray cavities, while X-ray micro-calorimetric observations from Athena could establish if the motion of the cold and warm gas is dominated by large-scale motions of the surrounding ICM.