PaulP: "So where is your predictive model of chaos?"
Again, our best example of a "predictive model of chaos" is modern weather prediction, now fairly accurate out to 10 days. Weather is chaotic, but because its also deterministic, we diligently improve forecasting.
Its not an original idea to combine predictive models, but quite standard in professional Weather Prediction. Since that is further along than us here, look at this page for an idea how ENSO could soon enough aggregate models and learn to synergize them. For now, you need only keep open to the idea that combining ENSO Models is a reasonable approach. I proposing that a Combined Model may be better predictive than yours alone.
Be patient, let me get to work better describing a Combined ENSO Model in the weeks to come. TIA if you have helpful links to any existing up-to-date ENSO model lists. I have seen a handful of Models, mentioned here and there, ranging from major geophysical institutions with many researchers, now running multi-physics solvers on supercomputers for decades, to your own model as offered, needing to be compiled.
It won't be hard to take basic predictions, to average them, or have models "vote", and tweak the combining algorithm over time. Of course, there may be emerge some dominant single model that is right more often than any combination of discrete models, but that model itself will likely be the most broadly comprehensive internally, combining and accounting for the most critical factors.
As for the ENSO sensor data sets, I have only just begun to validate (or not) the Lunisolar Noise Hypothesis. I start from the heuristic that a buoy or satellite sensor picks up a constant churn of tidal and wave sea states, plus sensor noise, as it also seeks imperfectly to detect desired long period state information. You also speculate over this same noisy data, and no analysis is yet final. You are ideally prepared to pivot and filter Lunisolar Noise from the data, should that prove to be helpful.
Here is starting information of Lunisolar Third Body Effect on orbiting satellites; 0.7m variation per orbit, comparable or greater than open ocean sea-surface tide range.
Perturbations in orbital elements of a low earth orbiting satellite
Eshagh and Najafi Alamdari 2005
[Heydt et al 2021] as quoted, is in good agreement with what I have been asserting about ENSO here.