Obtaining models that can be used for flight control is of outmost importance to ensure reliable guidance and navigation of spacecrafts, like a Generic Parafoil Return Vehicle (GPRV). In this paper, we convert an existing, high-fidelity nonlinear model of the atmospheric flight dynamics of a GPRV to a Linear Parameter-Varying (LPV) form that enables high-performance navigation control design. Application of existing systematic conversion methods for such complicated nonlinear models often result in complex LPV representations, which are not suitable for controller synthesis. We apply and compare state-of-the-art conversion techniques on the GPRV model, including learning based approaches, to optimize the complexity and conservatism of the resulting LPV embedding. The results show that we can obtain an LPV embedding that approximates the complex nonlinear dynamics sufficiently well, where the balance between complexity, conservatism and model performance is efficiently chosen.