The history of neutrinos is laden with limitations on understanding imposed by complications in measurement. This applies quite noticeably to the ongoing study of the phenomenon of neutrino oscillation. With improvements in detector size and technology, as well as experiments taken pertinent data for decades now, the era of precision measurements of all of these remaining parameters is coming in the relatively near future, with GeV-scale accelerator-based experiments playing a leading role. This means that in the central estimation of (anti)neutrino energy on which the phenomenon depends, the modeling of what is produced in the interactions these particles have with the detector needs to be understood. In the particularly fascinating question of whether CP violation exists in the lepton sector, where the answer is found as a difference in oscillations for neutrinos and antineutrinos, the non-oscillation discrepancies need to be well-modeled. As they are unable to detect through electromagnetic processes, able to escape detectors without ever depositing energy, and produced disproportionately more in antineutrino than neutrino interactions at the GeV-scale, neutrons present a unique problem to energy estimation. Past measurements from MINERvA have demonstrated the ability to measure antineutrino interaction cross sections involving neutron production via the detection of neutron interactions in the detector. These, and preceding model-dependent, measurements have also shown that there are notable discrepancies in the modeling of such processes. This past work has been focused on the polystyrene tracker region of the MINERvA detector. For future experiments with nuclei significantly larger than Carbon, and even more so Hydrogen, such as the Argon target of the next generation kTon-scale neutrino oscillation experiment, DUNE, having these interactions in larger nuclei is critical. This thesis builds upon the reconstruction and analysis tools from past work to study the production of neutrons in 5 of MINERvA's different nuclear targets: CH, C, H2O, Fe, Pb. This culminates in the measurement of a differential cross section in muon transverse momentum for muon antineutrinos producing at least one neutron and a final state consistent with a quasielastic scattering (QE-like) off of one nucleon in the nucleus. The results show a general underprediction of all of the models in the true QE-rich regions for all of the targets and provide insight into how different aspects of different models may be performing better than others.