Thanks for the video on the AMO Gavin, I found it very interesting
It was a topic that was briefly discussed in the TWO Climate Forum last year. I realise you didn't go into any possible causes of this 60-ish year full cycle but it does seem to be a bit of a mystery as to what is behind it
One interesting point is that if you plot the full global annual SST (HADSST3) against the annual AMO index you get quite a high correlation of about 78% which goes up to 83% if you take 10 year rolling averages of HADSST3 and AMO index. As the area of the Atlantic wouldn't seem to be large enough to have that much effect on the full global average, my belief is that the AMO is not just a "local" phenomenon to the Atlantic but is some manifestation of a full global cycle as seen in the Atlantic
On a technicality, I think (?) the NOAA data chart you showed with all the negative anomalies between 1963-1995 is a detrended list which has the long term AGW signal taken out first so as to show the index more clearly.