By taking advantage of the trace approximation, one can gain an enormous computational advantage when solving for the global turbulent transport of impurities. In particular, this makes feasible the study of non-Maxwellian transport coupled in radius and energy, allowing collisions and transport to be accounted for on similar time scales, as occurs for fast ions. In this work, we study the fully-nonlinear ITG-driven trace turbulent transport of locally heated and injected fast ions. Previous results indicated the existence of MeV-range minorities heated by cyclotron resonance, and an associated density pinch effect. Here, we build upon this result using the t3core code to solve for the distribution of these minorities, consistently including the effects of collisions, gyrokinetic turbulence, and heating. Using the same tool to study the transport of injected fast ions, we contrast the qualitative features of their transport with that of the heated minorities. Our results indicate that heated minorities are more strongly affected by microturbulence than injected fast ions. The physical interpretation of this difference provides a possible explanation for the observed synergy when neutral beam injection (NBI) heating is combined with ion cyclotron resonance heating (ICRH). Furthermore, we move beyond the trace approximation to develop a model which allows one to easily account for the reduction of anomalous transport due to the presence of fast ions in electrostatic turbulence.