Balachandran et al. [Phys. Rev. Lett. 120, 200603 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.200603] presented a segmented XXZ spin chain with zero anisotropy in one half and a large anisotropy on the other half that gave rise to a spin current rectification which is perfect in the thermodynamic limit. Here we extend the previous study to segmented chains with interacting integrable as well as nonintegrable halves, considering even cases in which no ballistic transport can emerge in either half. We demonstrate that, also in this more general case, it is possible to obtain giant rectification when the two interacting half chains are sufficiently different. We also show that the mechanism causing this effect is the emergence of an energy gap in the excitation spectrum of the out-of-equilibrium insulating steady state in one of the two biases. Finally, we demonstrate that in the thermodynamic limit there is no perfect rectification when each of the two half chains is interacting.