PaulP:"All you seem to be doing is marginalizing any analysis that I am posting to the forum."
Sorry if it seems so. Your analysis here stands or falls on its own merits; its not for anyone to change that. From the start, I readily agreed with you there must be (at least weak) Lunisolar Forcing to geophysical oscillations. If here and there analysis divergent from yours occurs, no worry about you somehow "marginalizing" it apart from inherent (de)merits.
You are specially invited to challenge the role of Lunisolar Noise on ENSO sensor data. The more I review the various sensor data sources, like sea-surface data, the more I find Lunisolar signals really are mixed-in, in real-time. These are not necessarily Forcings of overall ENSO Periodicity, and correction factors will filter out much of the spurious content. I am not sure yet how much sensor data defects currently skews your Model's output, but the "Pukite Number" proposed begins to bear rigorously on that question.
You rightly ask for a better predictive model here to compare with yours, and I have presented one. Again, with analogy to the best weather prediction, composite prediction is proposed based on the leading ENSO-QBO Models, including yours; to the extent these Models first singly show significant predictive validation. Am currently reviewing the field of ENSO Models. No doubt you deeply know many of these, and that their strengths could prove synergistic. As sensor data for training improves, there will increasingly be powerful Connectionist ENSO Models, that are semantic Black Boxes; so its not just classic equations and geophysical heuristics in play.
This is a sound plan of yours- "if my model made a correct prediction of the next El Nino, an informed statistician will claim that that can happen just by chance, because even a random guess can be correct a fraction of the time. So then I will be asked to make another prediction, and then another, ... until somebody deems that an adequate significance level is achieved." Let that "somebody" be understood to be the "informed statistician".
Accurately predicting just a few ENSO cycles in advance would indeed achieve "an adequate significance level", especially if there are no major mispredictions and the Model nicely catches outlier events longer and shorter than average. Not just cycle-periods need prediction, but also the amplitude of events, and identifying emerging multi-typed El Niño classifications.
A new conjecture here- that if the Earth was sufficiently uniform geophysically, Lunisolar Forcing, in combination with inherent geophysical harmonics, would generate specific Chladni Patterns. Partial heuristic evidence is the striking polar hexagon on Saturn.
Finally, regarding how better to apply the Topological Insulator concept to Equatorial Kelvin Waves, the equatorial waveguide effectively acts as a quasi 1D line case, often topologically identified as an Edge, ergo an Edge-Wave medium for Edge-Modes, ie Anyons under Sonic Relativity-
1D anyons in relativistic field theory, Yamamoto, 2018.
The topological insulator medium to EKW is effectively all the surrounding space and matter around the confined waveguide (edge); North, South, above (atmosphere), and below (sea-bottom).