The PHENIX experiment has measured the production of pi(0)s in Au + Au collisions at root S-NN = 200 GeV. The new data offer a fourfold increase in recorded luminosity, providing higher precision and a larger reach in transverse momentum, p(T), to 20 GeV/c. The production ratio of eta/pi(0) is 0.46 +/- 0.01(stat) +/- 0.05(syst), constant with p(T) and collision centrality. The observed ratio is consistent with earlier measurements, as well as with the p + p and d + Au values. pi(0) are suppressed by a factor of 5, as in earlier findings. However, with the improved statistical precision a small but significant rise of the nuclear modification factor R-AA vs p(T), with a slope of 0.0106 +/-(0.0034)(0.0029) (Gev/c)(-1), is discernible in central collisions. A phenomenological extraction of the average fractional parton energy loss shows a decrease with increasing p(T). To study the path-length dependence of suppression, the pi(0) yield is measured at different angles with respect to the event plane; a strong azimuthal dependence of the pi(0) R-AA is observed. The data are compared to theoretical models of parton energy loss as a function of the path length L in the medium. Models based on perturbative quantum chromodynamics are insufficient to describe the data, while a hybrid model utilizing pQCD for the hard interactions and anti-de-Sitter space/conformal field theory (AdS/CFT) for the soft interactions is consistent with the data.