In this paper, we use higher order impedance boundary conditions (HOIBCs) for studying high frequency asymptotic two-dimensional (2-D) scattering of truncated aperture-generated electromagnetic fields from planar conducting surfaces coated by multiple layers of homogeneous bi-anisotropic media. The reflected field syntheses are carried out via asymptotic reduction of rigorous plane-wave spectral integrals, which are subsequently discretized and transformed to the spatial domain through use of a Gabor-based narrow-waisted (NW) Gaussian beam (GB) algorithm. In this discretized algorithm, the GB propagators are approximated by previously explored standard and modified (uniform) complex-source-point paraxial asymptotic techniques. Example applications are restricted to zeroth and second order IBCs for single- and multilayer complex coatings, with emphasis on the adaptation of the NW-GBs to the HOIBC launch conditions in the presence of localizing (e.g., focused and/or abruptly truncated) illumination. The results confirm that the previously established utility of the NW-GB algorithm with respect to accuracy and computational feasibility continues to hold for this fairly general combination of environmental complexity and strongly inhomogeneous (localizing) illumination.