By way of a history lesson, syndication date was originally designed to mean "last updated date" (specifically to support "what's changed" and OAI-PMH) but at some point this was changed to function as "record created date" as Chris describes (and as is described in the current "v1 & v2" documentation).
As the designer I find this mildly annoying but I have to concede that when it stopped working for a few months nobody seemed to notice but me, and I can see uses for the "record created date" approach also (especially since the bulk of DigitalNZ material does not tend to get updated).
In the strictest sense, I don't see how the DigitalNZ API will support OAI-PMH in it's current (v2 or v3) form unless you harvest every DigitalNZ record regularly.
But I don't think that you need to worry because historic newspapers are very rarely changed after being made available online. They also tend to be made available online in very large batches, which I assume will have the same or similar syndication date in DigitalNZ. So you might harvest nothing for months, then suddenly get 100,000 new records overnight.
Gordon