A novel security checkpoint concept has been proposed to address the continuing growth in passenger traffic that airports are experiencing globally. The new security checkpoint intends to employ Automated Guided Vehicles (AGVs) instead of conveyor belts for baggage tray transportation. However, the new concept poses new challenges to the classic Multi-Agent Path Finding (MAPF) problem due to its small environment and high agent density. The AGV fleet will thus have to effectively coordinate their paths to avoid gridlocks within the crowded security checkpoint environment. Firstly, this paper presents a detailed Agent-Based Model (ABM) to accurately represent the new automated security checkpoint and estimate its passenger throughput. Secondly, the paper presents a new MAPF algorithm for the AGV fleet: the Windowed Hierarchical Idle-Push (WHIP) algorithm. WHIP is a prioritised MAPF solver that uses Push-operations to efficiently resolve the bottlenecks of the automated security checkpoint, avoiding gridlock even at very high agent densities. Experimentally, WHIP achieves path efficiencies 5 percentage points higher than leading prioritised MAPF algorithms, while requiring only half the computational runtime. Using the WHIP algorithm, the automated security checkpoint is capable of achieving an 18% increase in passenger throughput with respect to existing security checkpoints using conveyor belts.