We have previously developed computationally efficient Gabor-based, narrow-waisted (NW), discretized Gaussian beam (GB) algorithms for the determination of the 3D vector fields radiated by 2D arbitrary vector planar aperture distributions. In the present paper, these algorithms are extended to tracking the aperture-generated GBs through polarization-sensitive reflection/transmission interactions with arbitrarily shaped 3D dielectric layers. The resulting tracking scheme is applied to predicting the performance of rotationally symmetric hemispherical and ogival missile radomes, which cover 2D plane truncated apertures on gimbaled (rotatable) platforms. Comparisons with measured data show satisfactory agreement with the analytic predictions.