In comment #10, I had a mistake in the algorithm that picks the "better" of the two SOI values of Darwin vs Tahiti. The following is the corrected figure.
It didn't really change much with respect to the intervals that show some divergence, but I thought to highlight the La Nina episode at 2000 at being much stronger in the model than in the data. This has something to do with the change of forcing behavior after 1980. The TSI became stronger on an 11 year cycle, and I added a linearly increasing forcing as well to the RHS. The impact of this ramping factor is to push the SOI into the positive La Nina territory.