Future Space-Air-Ground Integrated Networks (SAGINs) involving Low Earth Orbit (LEO) satellites are characterized by a high degree of mobility in all of the space, the air, and the ground segment -- leading to high in-segment and between-segment network topology dynamics. Mobility simulation in an integrated space and ground simulation model has thus been identified as one of the key challenges of future research. In this paper we demonstrate that such an integration can be achieved by picking a point in the center of the scenario, the Satellite Observer Position (SOP), and constructing an East-North-Up (ENU) tangential plane through it to arrive at an all-Cartesian coordinate system. Its construction is well-aligned with the needs of Vehicle-to-Satellite (V2S) between-segment channel modeling without sacrificing accuracy for in-segment communication -- and which lends itself well to large-scale, high-efficiency simulation of future SAGINs. We back our assumptions with a detailed study on the potential impact of loss of accuracy, demonstrating it to be negligible for most practical purposes in the target application domain. We demonstrate the potential of the presented fully-integrated approach in a small proof-of-concept simulation study where we investigate the impact of small position differences of air/ground nodes in their interplay with the space segment.