A comprehensive 3D model of the central 300 pc of the Milky Way, the Central Molecular Zone (CMZ) is of fundamental importance in understanding energy cycles in galactic nuclei, since the 3D structure influences the location and intensity of star formation, feedback, and black hole accretion. Current observational constraints are insufficient to distinguish between existing 3D models. Dust extinction is one diagnostic tool that can help determine the location of dark molecular clouds relative to the bright Galactic Center emission. By combining Herschel and Spitzer observations, we developed three new dust extinction techniques to estimate the likely near/far locations for each cloud in the CMZ. We compare our results to four geometric CMZ orbital models. Our extinction methods show good agreement with each other, and with results from spectral line absorption analysis from Walker et al. Our near/far results for CMZ clouds are inconsistent with a projected version of the Y. Sofue two-spiral-arms model, and show disagreement in position-velocity space with the S. Molinari et al. closed elliptical orbit. Our results are in reasonable agreement with the J. M. D. Kruijssen et al. open streams. We find that a simplified toy-model elliptical orbit that conserves angular momentum shows promising fits in both position-position and position-velocity space. We conclude that all current CMZ orbital models lack the complexity needed to describe the motion of gas in the CMZ, and further work is needed to construct a complex orbital model to accurately describe gas flows in the CMZ.