We present a statistical study of energetic heavy ion acceleration in the near-Earth magnetotail using observations from the Energetic Ion Spectrometer (EIS) onboard the Magnetospheric Multiscale (MMS) spacecraft. Although the EIS instrument does not measure ion charge state directly, we have inferred the dominant charge state of the suprathermal heavy ions (i.e., ~60-1000 keV He and C-N-O), using a previously-developed correlation analysis of the time-dependent flux response between different energy channels of different ion species. For specific events we have also distinguished adiabatic (charge-dependent) energization from non-adiabatic (mass-dependent) energization. This work uses observations from the MMS “Bursty Bulk Flows (BBF) Campaign” in August 2016, when high-energy-resolution “burst”-mode data are more frequently available, to examine the relative occurrence of adiabatic energization versus preferential energization of heavy ions. The results of this study demonstrate the utility and limitations of the cross-correlation technique that was applied. We find that the technique is consistently able to discern coarse charge states for heavy ions such as O^+/6+, He^+/++ (i.e., ionospheric versus solar wind sources), but that the more subtle job of uniquely determining adiabatic versus non-adiabatic behaviors for the ionospheric component (O⁺) is only sometimes achievable. The dynamics of Earth’s magnetotail are apparently too complex and variable to consistently accommodate our simple assumption for adiabatic behavior of energy/charge-ordered transport from a common source of particles.