The conditions for dust-density wave (DDW) excitation in strongly coupled, magnetized laboratory dusty plasmas are analyzed using the generalized hydrodynamic model. Incorporating ion streaming, collisions, and magnetic field effects, we derive the DDW dispersion relation, determine the critical ion Mach number for instability onset, and characterize the nature of the unstable modes. Strong coupling is found to significantly reduce the critical ion-streaming Mach number for instability onset compared to weak coupling. Ion magnetization introduces propagation anisotropy, which preferentially drives the instability, thereby acting as a directional filter. A wave energy analysis identifies an ion response parameter that characterizes the coherent coupling of ions to wave perturbations and serves as the governing control parameter of the system, establishing a unified criterion for the onset of DDW instability across coupling and magnetization regimes. These results demonstrate that the previously unexplored combined regime of strong coupling and ion magnetization gives rise to qualitatively new features: a lowered instability barrier and strong directional selectivity, that are absent when either effect is considered in isolation. The implications are discussed for laboratory magnetized complex plasma experiments, dust transport and mobilization in the edge regions of magnetic confinement fusion devices, and astrophysical dusty plasma environments.