Same here, Dara. These wordy narratives are often referred to as "just so" stories. They are built on a sequence of premises "just so" they start to make plausible sense. Whether they are actually correct is another matter. I include these articles so that we can use them to cite previous work should we make definite progress.
For now, this is my toe-hold to try to explain why the tidal data has the magic 2-year number, both in the biennial oscillations and in the delay differencing factor.
As my own variation of a "just so" story, I could hypothesize that the surface of the ocean is sloshing with a certain behavior, while the thermocline layer below is sloshing with a similar behavior, but delayed or lagged by two years. The difference between the two could be the maximally exposed sub-surface temperature leading to SST and atmospheric pressure changes. Whether this working hypothesis is valid, who knows? but it gives us some other ideas for data to look at.