Axion dark matter can undergo a highly efficient resonant conversion to radio photons deep in the magnetospheres of neutron stars. This process is triggered when the ambient plasma density roughly matches the axion mass, and results in an extremely narrow spectral line centered near the axion mass. In this talk I will discuss the latest attempt to observe this process, which exploits ~5 hours of observation of the Galactic Center in the 4-8 GHz frequency band taken with the Green Bank Telescope. This work incorporates significant improvements on the forward modeling of the radio signal and the interpretation of radio data, representing a major step toward the development of a comprehensive indirect axion search program in the radio band.