Bruce,
As I am still in the UK, I don't have much experience to be able to comment on the job market in NZ as my only exposure has been through contacting several recruitment agencies, companies directly and reading threads on this site.
However, I have managed secure an audit role in Chch from June. I got this by sending out my CV to various employers directly. I found this far more effective than going via recruitment agencies, who were not very helpful. They all told me that I would need to be in NZ in order to attend interviews.
In my opinion, I would recommend submitting your EOI, as once your application is successful and you have PR/WTR you will at least be marketable in NZ! Finding employment from outside of NZ is hard enough without the added complexity of asking employers to support a work permit application.
I say jump on the rollercoaster and see where it takes you. You can continue searching for jobs even while your application is in the pool, as if you find employment, your application will be fast tracked.
However, Im certain there are many others on this site that are far more experienced to comment on the NZ job market.