We present an archival analysis of Chandra X-ray observations for 12 nearby early-type galaxies hosting radio sources with radio power >1023W/Hz at 1.4GHz, similar to the radio power of the radio source in NGC4261. Previously, in a similar analysis of eight nearby X-ray and optically bright elliptical galaxies, Werner et al. found that NGC4261 exhibited unusually low central gas entropy compared to the full sample. In the central 0.3kpc of NGC4261, the ratio of cooling time to freefall time (tcool/tff) is less than 10, indicating that cold clouds may be precipitating out of the hot ambient medium and providing fuel for accretion in the central region. NGC4261 also hosts the most powerful radio source in the original sample. Because NGC4261 may represent an important phase during which powerful feedback from a central active galactic nucleus (AGN) is fueled by multiphase condensation in the central kiloparsec, we searched the Chandra archive for analogs to NGC4261. We present entropy profiles of those galaxies, as well as profiles of tcool/tff. We find that one of them, IC4296, exhibits properties similar to NGC4261, including the presence of only single-phase gas outside of r~2kpc and a similar central velocity dispersion. We compare the properties of NGC4261 and IC4296 to hydrodynamic simulations of AGN feedback fueled by precipitation. Over the course of those simulations, the single-phase galaxy has an entropy gradient that remains similar to the entropy profiles inferred from our observations.