PaulP: "...a direction that is completely meaningless to me"

Physical theories are distinguished as Non-Relativistic or Relativistic. Your assertions about ENSO were clearly non-relativistic. We are not just talking about Einstein's Relativity, but Galilean Relativity, which is more basic. It really is meaningful, but more complex.

I like your identification of geophysically situated oscillations as Standing Waves, but there is far more going on than the ideal case, when there is messy complex multi-excitations. Standing waves are resistant to forcing that is not harmonically resonant, but often do express their inherent Helmholtz harmonics by anharmonic excitations.

There is nothing in [Ray 2019] inconsistent with some actual Lunisolar forcing, plus Lunisolar "noise" overlaid on the data, better interpreted as Crosstalk. Ray is simply reporting actual measured data, not parsing it ontologically in a manner beyond the scope of simple description.

At some point, hopefully, the Lunisolar Crosstalk Hypothesis, and applicable advanced ideas in Relativity, QM, and Thermodynamics, as invoked here in passing, can all acquire meaning to you, even if you still disagree.

I am certainly learning a lot here, so the understood meanings are growing.