This paper deals with the short-pulse radiation of three-dimensional (3-D) vector electromagnetic fields from arbitrarily polarized large two-dimensional (2-D) truncated aperture distributions, which are parameterized in terms of narrow-waisted ray-like pulsed Gaussian basis beams centered on a discretized Gabor lattice in a four-dimensional (4-D) configuration-spectrum phase space. The study extends our previous Gabor-based investigation of time-domain (TD) short-pulse radiation of 2-D fields from 1-D large truncated apertures with nonphased, linearly phased (delayed) and nonlinearly phased focusing aperture field profiles . We begin with, and summarize, a Gabor-based frequency domain (FD) formulation of the 2-D aperture problem which has been presented and tested elsewhere, but we include additional numerical examples for validation and quality assessment. As done by Galdi, Felsen and Castañon (see ibid., vol 49, p. 1322-32, Sept. 2001) we access the time domain by Fourier inversion from the FD, starting from the initial 3-D space-time Kirchhoff formulation (whose numerical integration furnishes reference solutions), and then passing on to Gabor-parameterized field representations in terms of pulsed beam (PB) wavepackets which are launched by linearly and nonlinearly phase-delayed focusing aperture distributions. Example calculations and comparisons with numerically generated reference data serve to calibrate the Gabor-PB algorithms and assess their domains of validity.