An 852 nm semiconductor laser is experimentally subjected to phase-conjugate time-delayed feedback achieved through four-wave mixing in a photorefractive (BaTiO3) crystal. Permutation entropy (PE) is used to uncover distinctive temporal signatures corresponding to the sub-harmonics of the round-trip time and the relaxation oscillations. Complex spatiotemporal outputs with high PE mostly upwards of ∼0.85 and chaos bandwidth (BW) up to ∼31GHz are observed over feedback strengths up to 7%. The low-feedback region counterintuitively exhibits spatiotemporal reorganization, and the variation in the chaos BW is restricted within a small range of 1.66 GHz, marking the transition between the dynamics driven by the relaxation oscillations and the external cavity round-trip time. The immunity of the chaos BW and the complexity against such spatiotemporal reorganization show promise as an excellent candidate for secure communication applications.