Existing low-Earth-orbit (LEO) communication link analyses face two main challenges: (1) limited accuracy of 3D atmospheric refractivity reconstructed from sparsely sampled radiosonde data, and (2) numerical instability in previous non-uniform plane-wave ray-tracing algorithms (i.e., underflow under standard double precision), where non-uniform plane waves inevitably arise at complex-valued dielectric interfaces, is caused by extremely small atmospheric loss terms. To address these issues, we reconstruct a high-resolution 3D complex-valued refractivity model using numerical weather prediction data, and develop a fast and numerically stable non-uniform plane-wave ray tracer. The method remains stable in double precision and delivers a 24-fold speedup over high-precision benchmarks. Comparisons show that boresight-error deviations and path-loss differences between the rigorous method and the uniform-plane-wave approximation remain negligible, even under heavy precipitation. Although rays in a lossy atmosphere experience different phase- and attenuation-direction vectors-forming non-uniform plane waves-the resulting effective attenuation along the path is nearly identical to that predicted by the uniform-plane-wave model. These findings justify the continued use of uniform-plane-wave ray tracing in practical LEO link analyses.