I was kind of evasive in answering Jim's question:
> "What happens if you remove the periods of these singular, episodes from your QBO-TSI-CW fitting or is that what you’re about to do?"
I will end up trying this, and the way that I propose to do it is worth sharing beforehand. My idea is to fit the model as before but when calculating the correlation coefficient, set the model and data values to zero at intervals from 0 to 3 years after a massive volcanic eruption. By setting it to zero, there is no contribution to the correlation within those intervals. Then after a fit is achieved, take a look at the residual within those intervals and it should always show an obvious cooling spike according to the current thinking WRT stratospheric aerosol reflection.
There are about 7 significant eruptions to include and that would remove about 7*3=21 years from a 135 year span of observations, which isn't that aggressive. The removal of that noise more than makes up for the reduction in available fitting data, and so a better (as in "truer" to pure ENSO dynamics) model will likely result.