I recently archived the paper to ARXIV and submitted to PRL.
Get the paper here from ARXIV as a PDF.
The nearly year-long investigation is time-lined and outlined here.
The final model fit:

Fig 1: Figure from the paper. When the correlation reached 0.8, I thought it might be the right time to stop. The noise in the Darwin or Tahiti time-series was the limiting factor in how good the fit could eventually become.
Thanks for the good comments!
One application of the model described below