With cadmium zinc telluride's (CZT) success as a gamma and x-ray detector material, there is need for high-quality, monocrystalline CZT in large volumes. Bridgman and gradient freeze growth methods have consistently produced material containing significant amounts of micron-sized, tellurium-rich inclusions, which are detrimental to device performance. These inclusions are believed to arise from a morphological instability of the growth interface driven by constitutional undercooling. Repeatedly rotating the crucible back and forth via the accelerated crucible rotation technique (ACRT) has been shown to reduce the size and number of inclusions. Via numerical techniques, we analyze the impact of two different applied temperature gradients, 10 K/cm and 30 K/cm, on the flow, temperature, tellurium distribution, and undercooling during growth with and without applied ACRT. Under growth without rotation, a higher axial thermal gradient results in stronger thermal-buoyancy driven flows, faster interface growth velocity, greater tellurium segregation, and stronger undercooling. ACRT improves the stability of the growth interfaces for both systems; however, contrary to conventional wisdom, the case of the shallow thermal gradient is predicted to exhibit a more stable growth interface, which may result in fewer inclusions and higher quality material.