Daniel, Interesting plots. I don't know if I will be able to articulate this clearly; but it may be that the reason for the scatter plot going in all directions is that the correlations go in both the forward and reverse temporal directions.
By this I mean that it is hard to separate measures that are the result of a *past* ENSO disturbance from the ones that are an indicator of a *future* ENSO disturbance.
The **xcorr** plot is one of the most useful in trying to pin down the causality. But if I am reading that right, the cross-correlation has a peak of around 100 months as a lag or 250 months as a lead (or vice versa depending how it is defined).
With leads and lags on that time frame, the causality becomes even more difficult to disentangle. Yet, since the correlations are still quite weak and erratic as you say, these could just as well all be spurious peaks.
So I agree with you that the scatter plot and the last cross correlation plot are the ones to further analyze.