Measurements of neutral pion (pi(0)) production at midrapidity in root s(NN)=200 GeV Au+Au collisions as a function of transverse momentum, p(T), collision centrality, and angle with respect to reaction plane are presented. The data represent the final pi(0) results from the PHENIX experiment for the first RHIC Au+Au run at design center-of-mass energy. They include additional data obtained using the PHENIX Level-2 trigger with more than a factor of 3 increase in statistics over previously published results for p(T)>6 GeV/c. We evaluate the suppression in the yield of high-p(T) pi(0)'s relative to pointlike scaling expectations using the nuclear modification factor R-AA. We present the p(T) dependence of R-AA for nine bins in collision centrality. We separately integrate R-AA over larger p(T) bins to show more precisely the centrality dependence of the high-p(T) suppression. We then evaluate the dependence of the high-p(T) suppression on the emission angle Delta phi of the pions with respect to event reaction plane for seven bins in collision centrality. We show that the yields of high-p(T) pi(0)'s vary strongly with Delta phi, consistent with prior measurements 1,2. We show that this variation persists in the most peripheral bin accessible in this analysis. For the peripheral bins we observe no suppression for neutral pions produced aligned with the reaction plane, whereas the yield of pi(0)'s produced perpendicular to the reaction plane is suppressed by a factor of similar to 2. We analyze the combined centrality and Delta phi dependence of the pi(0) suppression in different p(T) bins using different possible descriptions of parton energy loss dependence on jet path-length averages to determine whether a single geometric picture can explain the observed suppression pattern.