Expanding upon the work of Way & Srivastava we demonstrate how the use of training sets of comparable size continue to make Gaussian process regression (GPR) a competitive approach to that of neural networks and other least-squares fitting methods. This is possible via new large-size matrix inversion techniques developed for Gaussian processes (GPs) that do not require that the kernel matrix be sparse. This development, combined with a neural-network kernel function appears to give superior results for this problem. Our best-fit results for the Sloan Digital Sky Survey (SDSS) Main Galaxy Sample using u, g, r, i, z filters gives an rms error of 0.0201 while our results for the same filters in the luminous red galaxy sample yield 0.0220. We also demonstrate that there appears to be a minimum number of training-set galaxies needed to obtain the optimal fit when using our GPR rank-reduction methods. We find that morphological information included with many photometric surveys appears, for the most part, to make the photometric redshift evaluation slightly worse rather than better. This would indicate that most morphological information simply adds noise from the GP point of view in the data used herein. In addition, we show that cross-match catalog results involving combinations of the Two Micron All Sky Survey, SDSS, and Galaxy Evolution Explorer have to be evaluated in the context of the resulting cross-match magnitude and redshift distribution. Otherwise one may be misled into overly optimistic conclusions.