We have computed obscured active galactic nuclei (AGN) redshifts using the XZ method, adopting a broad treatment in which we employed a wide-ranging data set and worked primarily at the XZ counts sensitivity threshold, culminating with a redshift catalog containing 121 sources that lack documented redshifts. We considered 363 obscured AGN from the Chandra Source Catalog Release 2.0, 59 of which were selected using multiwavelength criteria while 304 were X-ray selected. One third of the data set had crossmatched spectroscopic or photometric redshifts. These sources, dominated by low-z and low-N H AGN, were supplemented by 1000 simulations to form a data set for testing the XZ method. We used a multilayer perceptron neural network to examine and predict cases in which XZ fails to reproduce the known redshift, yielding a classifier that can identify and discard poor redshift estimates. This classifier demonstrated a statistically significant ∼3σ improvement over the existing XZ redshift information gain filter. We applied the machine-learning model to sources with no documented redshifts, resulting in the 121 source new redshift catalog, all of which were X-ray selected. Our neural network’s performance suggests that nearly 90% of these redshift estimates are consistent with hypothetical spectroscopic or photometric measurements, strengthening the notion that redshifts can be reliably estimated using only X-rays, which is valuable to current and future missions such as Athena. We have also identified a possible Compton-thick candidate that warrants further investigation.