The potential for smuggling special nuclear material (SNM) into the United States is a major concern to homeland security, so federal agencies are investigating a variety of preventive measures, including detection and interdiction of SNM during transport. One approach for SNM detection, called active interrogation, uses a radiation source, such as a beam of neutrons or photons, to scan cargo containers and detect the products of induced fissions. In realistic cargo transport scenarios, the process of inducing and detecting fissions in SNM is difficult due to the presence of various and potentially thick materials between the radiation source and the SNM and the practical limitations on radiation source strength and detection capabilities. Therefore, computer simulations are being used, along with experimental measurements, in efforts to design effective active interrogation detection systems. The computer simulations primarily consist of simulating radiation transport from the source to the detector region(s). Although the Monte Carlo method is predominantly used for these simulations, difficulties persist related to calculating statistically meaningful detector responses in practical computing times, thereby limiting their usefulness for design and evaluation of practical active interrogation systems. In previous work, the benefits of hybrid methods that use the results of approximate deterministic transport calculations to accelerate high-fidelity Monte Carlo simulations have been demonstrated for source-detector-type problems. In this work, hybrid methods are applied and evaluated for three example active interrogation problems. Additionally, a new approach is presented that uses multiple goal-based importance functions depending on a particle's relevance to the ultimate goal of the simulation. Results from the examples demonstrate that the application of hybrid methods to active interrogation simulations dramatically increases their calculational efficiency.