In practice, this equilibrium ellipsoid does not develop because of the rotation of Earth, the Coriolis acceleration and the fact that the tidal wave feels the ocean bottom and it is subject to friction. Going beyond the equilibrium theory of the tide, the dynamic theory of tides (developed by Euler, Laplace and Bernoulli) includes all these concepts (friction, inertia, Coriolis, land masses,...) and provides a better approximation to the observed tides.
My recommendation to understand tidal constituents is to use some decent tidal harmonic analysis package like t_tide for Matlab, which is likely to be the tool that NOAA is using to generate their harmonic constituents in the first place. If you really want to get into the details, then the best option is to go to the still likely best source available. That will the 1973 book "The Analysis of Tides" by G. Godin.
Pawlowicz, R., B. Beardsley, and S. Lentz, "Classical Tidal Harmonic Analysis Including Error Estimates in MATLAB using t_tide", Computers and Geosciences, 28, 929-937 (2002).
Godin, G. (1973). The analysis of tides., by Godin, G.. Liverpool (UK): Liverpool University Press, 264 p.