Stable detection of high-speed dim point targets remains a key performance bottleneck for space-based infrared detection systems. During non-propulsive flight, such targets exhibit extremely weak infrared emissions, high velocities, and low imaging SNR, which severely limits the persistent detection capability of Geostationary/High Earth-orbit platforms and motivates exploitation of the slant-to-space geometry available to low-Earth-orbit (LEO) platforms. This research formulates the problem from the physical imaging chain of a LEO infrared system and develops a multi-parameter joint optimization model that systematically integrates target-background radiation, optical imaging design, and system-level physical constraints. At its core is a normalized, weighted multiplicative merit function that enables global optimization of key system parameters, including spectral bandwidth, center wavelength, detector operating temperature, optical angular resolution, aperture diameter, and optical system temperature. Parameter optimization and performance simulations based on a representative LEO long-wave infrared system configuration show that, compared with the pre-optimization baseline, the average detection sensitivity improves (i.e., NEI decreases) by 68.372W/sr@4000km when the tangent height is below 40km; by 22.162W/sr@4000km for 40-60km; and by 1.438W/sr@4000km for 60-80km; above 80km, where background effects weaken, the improvement becomes negligible. The optimized system enables stable detection of high-speed dim point targets during the non-propulsive phase, achieving a best-case detection sensitivity of 1.036W/sr@4000km. This research provides both a theoretical foundation and a practical pathway for system-level optimization of LEO long-wave infrared detection systems.