This is part II of a two-part paper. Part I presented a universal Birkhoff
theory for fast and accurate trajectory optimization. The theory rested on two
main hypotheses. In this paper, it is shown that if the computational grid is
selected from any one of the Legendre and Chebyshev family of node points, be
it Lobatto, Radau or Gauss, then, the resulting collection of trajectory
optimization methods satisfy the hypotheses required for the universal Birkhoff
theory to hold. All of these grid points can be generated at an
O(1) computational speed. Furthermore, all Birkhoff-generated
solutions can be tested for optimality by a joint application of Pontryagin's-
and Covector-Mapping Principles, where the latter was developed in Part~I. More
importantly, the optimality checks can be performed without resorting to an
indirect method or even explicitly producing the full differential-algebraic
boundary value problem that results from an application of Pontryagin's
Principle. Numerical problems are solved to illustrate all these ideas. The
examples are chosen to particularly highlight three practically useful features
of Birkhoff methods: (1) bang-bang optimal controls can be produced without
suffering any Gibbs phenomenon, (2) discontinuous and even Dirac delta covector
trajectories can be well approximated, and (3) extremal solutions over dense
grids can be computed in a stable and efficient manner