This paper examines the control of an autonomous underwater vehicle (AUV) with a deployable energy-harvesting kite for oceanographic observation and surveillance. The proposed design and control strategies specifically address objectives of achieving high-payload, long-endurance AUV operation through the deployment of an energy-harvesting kite while the AUV is anchored to the seabed, followed by the retraction of the kite for continued operation of the AUV. While deployed, the kite executes power-augmenting cross-current flight motions, using a hierarchical controller. When the AUV is in motion and the kite is retracted, a dynamic programming-based controller is used to select charging locations that minimize total charging time when traversing a prescribed mission path. Focusing on oceanographic observation along a Gulf Stream transect, using a hindcast model of the Gulf Stream current resource, the paper demonstrates the efficacy of the proposed control approach, as compared to several non-optimized alternatives.