> " still lower than the 6-month lag autocorrelation of the anomaly itself "
This means that an anomaly analysis, as in "dead-reckoning" based on its past history, works better for prediction than trying to extract something based on external link strengths.
This makes sense if the ENSO phenomena is more of an internal phenomenon fed by equatorial waters and winds, than something triggered by external links from regions spatially separated from the equatorial Pacific.
That works as a kind of a null hypothesis. Unless one can find a link that is stronger than the autocorrelation of the ENSO signal itself, it will be hard to get buy-in that it is a better predictor.