Designing aerial robots for specialized tasks, from perching to payload delivery, requires tailoring their aerodynamic shape to specific mission requirements. For tasks involving wide flight envelopes, the usual sequential process of first determining the shape and then the motion planner is likely to be suboptimal due to the inherent nonlinear interactions between them. This limitation has been motivating co-design research, which involves jointly optimizing the aerodynamic shape and the motion planner. In this paper, we present a general-purpose, gradient-based, nested co-design framework where the motion planner solves an optimal control problem and the aerodynamic forces used in the dynamics model are determined by a neural surrogate model. This enables us to model complex subsonic flow conditions encountered in aerial robotics and to overcome the limited applicability of existing co-design methods. These limitations stem from the simplifying assumptions they require for computational tractability to either the planner or the aerodynamics. We validate our method on two complex dynamic tasks for fixed-wing gliders: perching and a short landing. Our optimized designs improve task performance compared to an evolutionary baseline in a fraction of the computation time.