This paper assesses the feasibility of observing the gyro-phase drift in the Auburn Magnetized Dusty Plasma Experiment [MDPX, described by Thomas et al., Plasma Phys. Controlled Fusion 54, 124034 (2012)]. The gyro-phase drift arises when a dust grain does not instantaneously reach the in-situ-equilibrium grain charge during gyro-synchronous grain-charge modulation. Koepke et al. [J. Plasma Phys. 79, 1099 (2013)] first suggested using MDPX to observe the gyro-phase drift, and here we use a single-particle trajectory tracker with an iterative velocity solver, using a fixed timestep for grain motion and an adaptive time step for grain charging, to consider all relevant dust grain forces to assess gyro-phase drift arising from gradual inhomogeneity. Additionally, the semi-analytic theory developed by Walker et al. [J. Plasma Phys. 80, 395 (2014)] predicts dust grain motion in abrupt inhomogeneity for MDPX-relevant conditions. We compare three grain-charging models with each other and with the single-particle trajectory tracker and found to predict distinctly different trajectories depending on the treatment of neutral drag and flowing ions. The measurement thresholds for Particle Tracking Velocimetry permit gyro-phase drift detection in MDPX for the abrupt inhomogeneity, given sufficiently large enough UV photoelectron flux (fuv/[nevthe]>0.01) and low enough neutral gas pressure (less than one mTorr). The Orbit-Motion-Limited charge model and the charge models developed by Patacchini et al. [Phys. Plasmas 14, 062111 (2007)] and Gatti and Kortshagen [Phys. Rev. E 78, 046402 (2008)] can, in principle, be distinguished by gyro-phase drift in the abrupt inhomogeneity, but large magnetic fields, large UV photoelectron flux, and low neutral gas pressure are required. Gyro-phase drift for a gradual inhomogeneity in the ratio ne/ni, arising from the presence of a radial electric field, is predicted to be undetectable.