Hi Bob, those are great questions, and the short answer is that I don't know. Starting with the PDO, it's important to note that the PDO represents, in part, a response to ENSO as well as other processes, and so it is difficult to disentangle the effects of the PDO on ENSO from the response of the PDO to ENSO. This article gives a nice review of the PDO for practitioners in the field. 

However, North Pacific variability is known to impact ENSO through the Pacific Meridional Mode (PMM) - I recommend reviewing that guest post by Dr. Daniel Vimont. This article suggests that the PMM may be important for double-dip La Ninas and presumably three-year La Ninas as well. I haven't looked closely to see if there could be a PMM-like connection with the current forecast. 

I also will note that the tropical Pacific has experienced a multidecadal La Nina-like trend with cooling temperatures in the tropical eastern Pacific and a strengthening Walker circulation that opposes expectations under increasing greenhouse gases. Could this reflect either natural variability or a radiatively forced response that has impacted the frequency of La Nina? We don't fully understand these recent trends, so I cannot give you an answer. 

Regarding the AMO, there have been numerous studies suggesting that warming in the tropical North Atlantic is linked with La Nina occurrence (like here, here, and here). So, it is possible that there is an Atlantic connection, though it would take more investigation to firmly establish the causal links. 

The bottom line is that it is intriguing that the NMME models have seen this signal for persisting La Nina conditions despite the absence of strong El Nino that typically precedes multi-year La Ninas. So, is this signal originating from other basins? Again, I don't have the answer, but it's an intriguing question.