We present a stochastic, two-dimensional model of centrosomal microtubule (MT) organization during cell polarization that couples centrosome positioning, MT length dynamics, and polarity factor (PF) transport. Our model incorporates two essential mechanisms: (1) active transport of diffusing PFs along MTs to plus-ends, where they locally stabilize MTs by enhancing growth and suppressing catastrophe; and (2) growing MTs at the cell boundary generate pushing forces that drive centrosome movement. Numerical simulations reveal that robust MT network polarization emerges from the synergy between PF-mediated regulation and MT-driven centrosome motility. This synergy establishes a composite positive feedback loop, in which the PF-mediated positive feedback loop and centrosome decentering mutually reinforce each other to amplify initial asymmetries. Additionally, we identify a distinct, independent positive feedback loop underlying spontaneous centrosome decentering, which alone suffices to ensure robust polarization. Notably, a MT network with a fixed centrosome fails to generate significant anisotropy, underscoring that centrosome positioning is not merely a consequence but an active determinant of MT organization. These findings provide a mechanistic framework integrating cytosolic PF-mediated MT organization regulation with centrosome dynamics in cell polarity establishment.