This paper explores the complexities of designing a multi-element transceiver system for free-space optical (FSO) communication between unmanned aerial vehicles (UAVs). We formulate the problem of placing optoelectronic transmitters (TXs, e.g., lasers) and receivers (RXs, e.g., photodetectors (PDs)) on a transceiver plane. The formulation aims to maximize the Signal-to-Interference-plus-Noise Ratio (SINR) among two hovering UAVs. We prove that the optimum tiling of TX and RX elements on an in-band full-duplex (IBFD) transceiver is NP-complete. Using a genetic algorithm (GA), we investigate solutions to the optimum tiling problem for various transceiver shapes, including circular, hexagonal, rectangular, and square shapes. The optimum SINR does not occur at a fixed coverage ratio but instead varies non-monotonically with link range. For each transceiver shape, we find diverse tiling patterns until the grid size becomes equal to the beam footprint. Furthermore, we identify unique laser placement patterns for each transceiver shape that sustain optimal performance over varying link ranges. Despite the increasing number of TXs (28 at 40 m to 52 at 100 m for square shape transceiver), the GA finds the same optimized tiling geometry, allowing the design to scale across distances for multiple platforms without need for mechanical steering.