PaulP: "So, which is a better ENSO model? Mine or this ML version?"

Let measured predictive success decide the question. I agree with you below.

PaulP on ML Version: "a great addition to open-source climate science. "

Caution: Machine Learning is also susceptible to overfitting and underfitting, caused by imperfect data.

Here is NOAA prediction as reference-model. They seem to avoid overfitting and underfitting risk better than simple models dependent on narrower data-sets.