Perching on the moving platforms is a promising solution to enhance the endurance and operational range of quadrotors, which could benefit the efficiency of a variety of air-ground cooperative tasks. To ensure robust perching, tracking with a steady relative state and reliable perception is a prerequisite. This paper presents an adaptive dynamic tracking and perching scheme for autonomous quadrotors to achieve tight integration with moving platforms. For reliable perception of dynamic targets, we introduce elastic visibility-aware planning to actively avoid occlusion and target loss. Additionally, we propose a flexible terminal adjustment method that adapts the changes in flight duration and the coupled terminal states, ensuring full-state synchronization with the time-varying perching surface at various angles. A relaxation strategy is developed by optimizing the tangential relative speed to address the dynamics and safety violations brought by hard boundary conditions. Moreover, we take SE(3) motion planning into account to ensure no collision between the quadrotor and the platform until the contact moment. Furthermore, we propose an efficient spatiotemporal trajectory optimization framework considering full state dynamics for tracking and perching. The proposed method is extensively tested through benchmark comparisons and ablation studies. To facilitate the application of academic research to industry and to validate the efficiency of our scheme under strictly limited computational resources, we deploy our system on a commercial drone (DJI-MAVIC3) with a full-size sport-utility vehicle (SUV). We conduct extensive real-world experiments, where the drone successfully tracks and perches at 30~km/h (8.3~m/s) on the top of the SUV, and at 3.5~m/s with 60{\deg} inclined into the trunk of the SUV.